What is the gradient function of f(x)=x^3+2x?. Is it g(x)=x3+2 or g(x)=((x+h)^3+2(x+h)-(x^3+2x)) /h

1 Answer
Jim G.
Feb 5, 2018

#f'(x)=((x+h)^3+2(x+h)-(x^3+2x))/h#

Explanation:

#"the definition of the gradient function "#

#"from "color(blue)"first principles"# is.

#f'(x)=lim_(hto0)(f(x+h)-f(x))/h#

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

#rArrf'(x)=lim_(hto0)((x+h)^3+2(x+h)-(x^3+2x))/h#

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