Question #2199e

2 Answers
Somebody N.
Nov 15, 2017

#f^'(x)=3x^2+2#

Explanation:

It appears you are trying to add the derivative ( gradient function) onto the original function. You can't do that. To find the gradient function you just differentiate #f(x)=x^3+2x#.

#f(x)=x^3+2x#

#d/dx (x^3+2x)=3x^2+2#

So gradient function is: #f^'(x)=3x^2+2#

Jim G.
Nov 15, 2017

#f'(x)=3x^2+2#

Explanation:

#•color(white)(x)m_(color(red)"tangent")=f'(x)#

#"that is the gradient function is the derivative of "f(x)#

#"differentiate using the "color(blue)"power rule"#

#•color(white)(x)d/dx(ax^n)=nax^(n-1)#

#rArrf'(x)=3x^2+2larrcolor(blue)"gradient function"#

#"the gradient function allows us to calculate the"#
#"gradient of the tangent at any point on the curve"#

#"example where x = 1"#

#x=1toy=1+2=3rArr(1,3)#

#rArrf'(1)=3(1)^3+2=5=m_(color(red)"tangent")" at "(1,3)#

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