Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

Using the definition of a derivative how do you calculate the derivative of #f(x) = x^2 + x#?

1 Answer

May 18, 2015

#lim_{h->0}(f(x+h)-f(x))/h=lim_{h->0}((x+h)^2+(x+h)-x^2-x)/h#

#=lim_{h->0}(x^2+2xh+h^2+h-x^2)/h=lim_{h->0}(h(2x+h+1))/h#

#=lim_{h->0}(2x+1+h)=2x+1#.

Related questions

What is the limit definition of the derivative of the function #y=f(x)# ?
Ho do I use the limit definition of derivative to find #f'(x)# for #f(x)=3x^2+x# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(x+3)# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=1/(1-x)# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=x^3-2# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=1/sqrt(x)# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=5x-9x^2# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(2+6x)# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=mx+b# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=c# ?

See all questions in Limit Definition of Derivative

Impact of this question

1860 views around the world

You can reuse this answer
Creative Commons License