Summary of Differentiation Rules

Key Questions

What is a summary of Differentiation Rules?

Power rule:
if $f(x) = x^n$ then $f'(x) = nx^(n-1)$

Sum rule:
if $f(x) = g(x)+h(x)$ then $f'(x) = g'(x)+h'(x)$

Product rule:
if $f(x) = g(x)h(x)$ then $f'(x) = g'(x)h(x) + g(x)h'(x)$

Quotient rule:
if $f(x) = g(x)/(h(x))$ then $f'(x) = (g'(x)h(x) - g(x)h'(x))/(h(x))^2$

Chain rule:
if $f(x) = h(g(x))$ then $f'(x) = h'(g(x))g'(x)$
Or:
$dy/dx=dy/(du)*(du)/dx$

For more information:
http://socratic.org/calculus/basic-differentiation-rules/summary-of-differentiation-rules

Plmz1221 · 1 · Aug 4 2014

Questions

What is a summary of Differentiation Rules?
What are the first three derivatives of $(xcos(x)-sin(x))/(x^2)$ ?
How do you find the derivative of $(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))$ ?
How do I find the derivative of $y= x arctan (2x) - (ln (1+4x^2))/4$ ?
How do you find the derivative of $y = s/3 + 5s$ ?
What is the second derivative of $(f * g)(x)$ if f and g are functions such that $f'(x)=g(x)$ and $g'(x)=f(x)$ ?
How do you calculate the derivative for $g(t)= 7/sqrtt$ ?
Can you use a calculator to differentiate $f(x) = 3x^2 + 12$ ?
What is the derivative of $ln(x)+ 3 ln(x) + 5/7x +(2/x)$ ?
How do you find the formula for the derivative of $1/x$ ?
How do you find the derivative for $2x^4-1$ ?
How do you differentiate $f(x)=5x^4-3x^2+2$ ?
How do you differentiate $f(x) = 260$ ?
How do you differentiate $x^3 + x^2 +10$ ?
How do you differentiate $(5-x^2)(x^3-3x+3)$ ?
How do you find the derivative of $f(x)=(1/x^2)$ ?
How do you find the derivative of $x^2-4$ and $x^2-3x+2$ ?
How do you find the derivative of the function $f(x)=-2x^-3+x^2-7$ ?
How do you find the derivative of $x+sqrt(x)$ ?
How to find the derivative of $x^4$ ?
How do you differentiate $f(x) = abs(5x-2)$ ?
What is the derivative of $y= x/pi$ ?
How do you find the first, second derivative of $3x^(2/3)-x^2$ ?
How do you find the derivative of $f(x)=x^2-5x+3$ ?
How do you find the derivative of $f(x)=x^ln(3)$ ?
How do you differentiate $d/dx 5^2x^2$ ?
How do you find the derivative of $sqrt(x^2+1)$ ?
How do you find the derivative of $4sqrt(x-3) + x^5/(2x)$ ?
How do you find the derivative of the function: $f(x) = x^3 - 3x^2 - 1$ ?
How do you find the derivative of the inverse of $y = 4x + 2x$ ?
How do you find the derivative of the inverse of $f(x)=7x+6$ ?
How can I find the derivative of the inverse of $f(x)= x^3+x+1$ at x=11?
How do you find the derivative of an inverse function of $f(x)=x^5+3x−2$ ?
How do you differentiate f(x) = sin(x²)?
How do you differentiate f(x) = x² ln(x) ?
How do you differentiate $f(x) = sin ( x² ln(x) )$ ?
How do you differentiate $f(x) = 2x cos(x²)$ ?
How do you differentiate $f'(x) = 2x log(x) + x$ ?
How do you differentiate $f(x) = [ (2x)/(log(x)) ] - [ x/(log²(x)) ]$ ?
How do you differentiate $f'(x) = cos( x² ln(x) ) * ( 2x ln(x) + x )$ ?
How do you differentiate $(x^2-5x+2)/root3x$ ?
How do you differentiate $g(w) = (w^n - 5^n) /n$ ?
How do you differentiate $(4x^-2) - 8x + 1$ ?
How do you differentiate $f(x)=x*e^(1-sqrt(x)*ln(x))$ ?
How do you differentiate $f(x)= 5/x^3 - 3/ x^(1/3)$ ?
How do you differentiate $1/sqrt(1-x^2)$ ?
How do you differentiate $y=x*sqrt(16-x^2)$ ?
How do you differentiate $f(x)= 2^(3x)$ ?
How do you differentiate $y= 1/x (sin^-5(x)) - x/3 (cos^3(x))$ ?
How do you differentiate $[sin[(3x+7)^2]^3]$ ?
How do you differentiate $sin^2(x)$ ?
How do you differentiate $y = -2 /root3x$ ?
How do you differentiate $y=3x^4-6x^3+x^2/8+5$ ?
How do you differentiate $2x^4 * 6^(3x)$ ?
How do you differentiate $[(2x^3) - (4x^2) + 3] / x^2$ ?
How do you differentiate $(4x)^3 * (2x)^6$ ?
How do you differentiate $(6x-5)^4$ ?
How do you differentiate $y = -7x*(-5/3)$ ?
How do you differentiate $y = -(1/x^2) - sqrtx + (1/2)$ ?
How do you differentiate $y = (x^3 + 4)(-x^6 + x^4)$ ?
How do you differentiate $y = (sqrt x + (1/2))(x^3 + x^(1/3))$ ?
How do you differentiate $y = (2x^3 + 4 )/( x + 7)$ ?
How do you differentiate $y = (x^(2/3) + 3) /( x^(1/5) + x)$ ?
How do you differentiate $(3+2x - x^2)^(1/2)$ ?
How do you differentiate $f(x) = 1 + 1/x + 7/x^2 + 1/x^3$ ?
How do you differentiate $y=(4x^2+5)(3x-5)$ ?
How do you differentiate $(1+x)^(1/x)$ ?
How do you differentiate $f(x) = (2x+1)(4-x^2)(1+x^2)$ ?
What is the derivative of $f(x)= log_3(3-2x)$ ?
What is the derivative of $y= ln abs(secx-tanx)$ for $x>0$ ?
What is the derivative of $f(x)=ln(e^(2x))$ ?
What is the derivative of $f(x)=ln(ln(x))$ ?
What is the derivative of $y=x/(x^3-1)$ ?
What is the derivative of $7y= e^(-x^2)$ ?
What is the derivative of $y= -e^(x^2+x-3)$ ?
What is the derivative of $y= (e^(ix)-e^(-ix) )/2$ ?
How do you find $(delf(x,y))/(dely)$ and $(delf(x,y))/(delx)$ of $f(x,y)=(yx^2-2y)/(2ye^x+y^-3)$ , using the quotient rule?
How do you find the derivative of $((x)^(1/2))(e^(x))$ ?
How do you find the derivative of $h(x) = ln(cosh(2x))$ ?
How do you find the derivative of $f(x) = 1/sqrt(x)$ ?
How do you find the derivative of $f(x)=x^3-5x^2+2x+8$ ?
How do you find the derivative of $(log^2(x))$ ?
How do you find the derivative of $x^(5/3) * ln(3x)$ ?
How do you find the derivative of $f(x)=x^3 - 5x^2 - 4x + 20$ ?
How do you find the derivative of $sinh^4(x)$ ?
How do you find the derivative of $3x² + 2sin(x - 5)$ ?
How do you find the derivative of $(x+1)^x$ ?
How do you find the derivative of $F(X)= tan^-1(E^(x*sinx))$ ?
How do you find the derivative of $((2x+1)^(5)/(x^(2)+1)^(1/2))$ ?
How do you find the derivative of $f(x) = x^4 - 3/4x^3 - 4x^2 +1$ ?
How do you find the derivative of $8^(2x)$ ?
How do you find the derivative of $4^(6x)$ ?
How do you find the derivative of $g(t)=(2t)^(sin(t))$ ?
How do you find the derivative of $f(x)=sin8x$ ?
How do you find the derivative of $x^(log(base5)(x))$ ?
How do you find the derivative of $f(x)= x^logx$ ?
How do you find the derivative of $y = (3x + 1)^2$ ?
How do you find the derivative of $(pi/2)sinx-cosx$ ?
How do you find the derivative of $f(x) = (x)(14^x)$ ?
How do you find the derivative of $(sin x)^cos x$ ?
How do you find the derivative $f(x)= 3x+2$ ?
What is the derivative of $e^a$ (a is any constant number)?
What is the derivative of $e^1$ ?
What is the derivative of $y = [(x-2)/k]^(1/2)$ where k is a constant?
What is the derivative of $1/x$ ?
What is the derivative of $4/x$ ?
What is the derivative of $e^2$ ?
What is the derivative of $c*(e^x)$ where c is a constant?
What is the derivative of $2$ ?
What is the derivative of $pi$ ?
What is the derivative of $picosx$ ?
What is the derivative of $picos((pit)/6)$ ?
What is the derivative of $x/2$ ?
What is the derivative of $x^2/5$ ?
What is the derivative of $e^(-kx)$ ?
What is the derivative of $i$ ?
What is the derivative of $y=x+a$ ?
What is the derivative of $b^x$ where b is a constant?
What is the derivative of $ln 5$ ?
What is the derivative of $2^(1/2) (x + 2)$ ?
What is the derivative of $y=-4$ ?
How do you find the first and second derivative of $x^2-2x-3$ ?
How do you find the derivative of $f(x) = x^(5/ 2) e^x$ ?
How do you find the derivative of $y=[(2-3x^2)^(1/2)](5x+2)$ ?
How do you find the derivative of $(x-3) /( 2x+1)$ ?
How do you find the derivative of $sin (cos(2t-5))$ ?
How do you find the derivative of $x$ ?
How do you find the derivative of $f(x)= x/(x-1)$ ?
How do you find the derivative of $f(x) = -2x^2.5 + 8x^5$ ?
How do you find the derivative of $y=10x^-2 + 3x^-4 - 6x$ ?
How do you find the derivative of $y= ( 2x sin x ) ^ 3x cos x$ ?
How do you find the derivative of $f(x) = (1/x)^x$ ?
How do you find the derivative of $g(t) = (e^-t + e^t)^3$ ?
How do you find the derivative of $y = x^(cos x)$ ?
How do you find the derivative of $ln(sec^2 * x)$ ?
How do you find the derivative of $y= (1+x^2)cot-1(2x)$ ?
How do you find the derivative of $y=x^4-3x^2+7x-2$ ?
How do you find the derivative of $F(x) = (sinx/(1+cosx))^2$ ?
How do you find the derivative of $f(x) = (2x-3) ^ -2$ ?
How do you find the derivative of $f(x) = (4x^3 + 2x) ^ - 4$ ?
How do you find the derivative of $root5(x^-5)$ ?
How do you find the derivative of $f(x)=x/(1 + x^2)$ ?
How do you find the derivative of $y= x^3*2^x$ ?
How do you find the derivative of $root3((6x+7))$ ?
How do you find the derivative of $y= e^(ex) ln x$ ?
How do you find the derivative of $y= log_4(x+e^x+e)$ ?
How do you find the derivative of $6(z^2+z-1)^-1$ ?
How do you find the derivative of $y=arcsin(5x+5)$ ?
How do you find the derivative of $y = (ln 2)^x$ ?
How do you find the derivative of $f(x) = ln(e^-x - x)$ ?
How do you find the derivative of $f(x) = (5x^2 + 11)e^(-21x)$ ?
How do you find the derivative of $y = (x^2 + sqrtx + 1 ) / x^(3/2)$ ?
How do you find the derivative of $f(x)=1/(x-1)$ ?
How do you find the derivative of $f(x)=sqrt(x+1)$ ?
How do you find the derivative of $ln(1+(1/x))$ ?
How do you find the derivative of $-2x(x^2+3)^-2$ ?
How do you find the derivative of $1/x$ ?
How do you find the derivative of $(1+x)^(1/x)$ ?
How do you find the derivative of $2x-1$ ?
How do you find the derivative of $1/(x^3-x^2)$ ?
How do you find the derivative of $1/(x+1)^2$ ?
How do you find the derivative of $e^(1/x)$ ?
How do you find the derivative of $1/x^2$ ?
How do you find the derivative of $f(x)=(1/x^2)$ ?
How do you find the derivative of $1/t^2$ ?
How do you find the derivative of $1/(1+x^4)$ ?
How do you find the derivative of $(tanx)^-1$ ?
How do you find the derivative of $sin^-1 * (5x)$ ?
How do you find the derivative of $csc^-1 (u)$ ?
How do you find the derivative of $ln((x+1)/(x-1))$ ?
How do you find the derivative of $arctan(1/x)$ ?
How do you find the derivative of $(2x-1)^3$ ?
How do you find the derivative of $1/sqrt (x-1)$ ?
How do you find the derivative of $sin^-1(x)$ ?
How do you find the derivative of $[e^x / (1 - e^x)]$ ?
How do you find the derivative of $4 / (x+3)$ ?
How do you find the derivative of $(1/(3x^2) - (5/(2x)))$ ?
How do you find the derivative of $1/(1- x)$ ?
How do you find the derivative of $1 / (sinx+cosx)$ ?
How do you find the derivative of $(x/(2x+1))$ ?
How do you find the derivative of $1/(1+x^2)$ ?
How do you find the derivative of $1/(x+1)$ ?
How do you find the derivative of $ln(1/x)$ ?
How do you find the derivative of $x^(1/x)$ ?
How do you find the derivative of $(X/(X^2+1))$ ?
How do you find the derivative of $1/(sec x - tan x)$ ?
How do you find the derivative of $1/cosx$ ?
How do you find the derivative of $1/x^5$ ?
How do you find the derivative of $sqrt(1-x^2)$ ?
How do you find the derivative of $sqrt(3x+1)$ ?
How do you find the derivative of $sqrt(1-2x)$ ?
How do you differentiate given $y=(secx^3)sqrt(sin2x)$ ?
How do you find the derivative of the inverse of $y = x^2 + 1$ ?
How do you find the derivative of the function: $f(x) = x^3 - 3x^2 - 1$ evaluated at x=3?
How do you differentiate $f(x) = -5x + 3$ ?
What is the derivative of $f(x)=5$ ?
What is the derivative of $x=1$ ?
How do you calculate the fourth derivative of $f(x)=2x^4+3sin2x+(2x+1)^4$ ?
If F(x) is a differentiable function, and $F(-1) = 5$ , $F'(-1) = 4$ and $(F^-1)(4) = 2/3$ then what is $(F^-1)'(5)$ ?
Let $f(x)= -35x-x^5$ and let g be the inverse function of f, how do you find a) g(0) b) g'(0) c) g(-36) d) g'(-36)?
If g is the inverse of f and if $f(x)=x^3-5x^2+2x-1$ , how do you calculate g'(-9) if the domain of f(x) is the set of integers less than 0? Thanks in advance for taking time to help me out. Steve?
How do you find $(f^-1)'(a)$ if $f(x)= x/sqrt{x-3}$ and a = 4?
How do you use the formula (ln f(x))'= f'(x) / f(x) to show that lnx and ln(2x) have the same derivative?
Let $f(x) = x^2 - 4x - 5$ , x > 2, how do you find the value of $(df^-1)/dx$ (or the derivative of the inverse of f(x)), at the point x = 0 = f(5)?
Given $f(x)= x^3 +2x -1$ , how do you find $1/ [f^(-1)(2)]$ ?
Let $f(x)=x^5+3x−2$ and let $f^-1$ denote the inverse of f, Then how do you find $(f^-1)'(2)$ ?
Question #56aac
Question #f6e45
Question #13d2c
Question #99f2e
How do you differentiate $f(x)=(x-2)/(x^4+1)$ ?
How do you differentiate $f(x)=(1/(1+x))^-1$ ?
How do you differentiate $f(x)=1/(1+x^2)^2$ ?
How do you differentiate $f(x)=x/(1+sqrtx)$ ?
How do you differentiate $f(x)=sqrt((1-x)/(1+x))$ ?
How do you differentiate $f(x)=sinx+cosx$ ?
How do you differentiate $f(x)=3sinx+2cosx$ ?
How do you differentiate $f(x)=xsinx+cosx$ ?
How do you differentiate $f(x)=xcosx-sinx$ ?
How do you differentiate $f(x)=sinx/x$ ?
How do you differentiate $f(x)=cos^2x$ ?
How do you differentiate $f(x)=sqrt(1-sin^2x)$ ?
How do you differentiate $f(x)=sqrt((1-sinx)/(1+sinx))$ ?
How do you differentiate $f(x)=cosx/sinx$ ?
How do you differentiate $f(x)=sin2x-cos3x$ ?
How do you differentiate $f(x)=sin(pi/x)$ ?
How do you differentiate $f(x)=sin(cos(3x))$ ?
How do you differentiate $f(x)=sinx^2/x^2$ ?
How do you differentiate $f(x)=cos^2x-cosx^2$ ?
Find the partial derivatives of $m = ln(qh-2h^ 2)+2e(q-h^2+3)^4-7$ ?
What is the formula for the $n$ th derivative of $f(x) = x^(1/2)$ ?
Question #d9dbd
Question #1d4dc
How to find the derivative of the following function: f(t)= 1/ 2t^3? Thank you
How do we differentiate $f(x)=sin^4(4x^2-6x+1)$ using chain rule?
Given that y=(k+x)cosx where k is a constant find d^2y\dx^2 +y and show that it's independent of k ?
Question #05dd5
We have $f:RR->RR,f(x)=|x|root(3)(1-x^2)$ .How to find maximum domain of differentiability?
Question #b49a3
Question #5ef69
What is the derivative of? : $sin^2(x/2) \ cos^2(x/2)$
What is the derivative of $sinx/tanx$ wrt $x$ ?
Question #4492c
Find dy/dx when (A) $y= sqrtlnx$ , (B) y= arctan 5x ?

Basic Differentiation Rules

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Power Rule
Chain Rule
Sum Rule
Product Rule
Proof of the Product Rule
Quotient Rule
Implicit Differentiation
Summary of Differentiation Rules
Proof of Quotient Rule

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Basic Differentiation Rules