Find the derivatives of the following function from the deﬁnition in terms of x, f(x) and f′(x).
g(x) = f(x)^2

Question

Find the derivatives of the following function from the deﬁnition in terms of x, f(x) and f′(x). 
g(x) = f(x)^2

anonymous · Answer

by the chain rule 
$$g'(x)=2f(x)f'(x)$$

anonymous · Answer

I can't use the chain rule yet on it

anonymous · Answer

Then use the product rule: So $$g'(x)=f(x)f'(x)+f'(x)f(x)$$

anonymous · Answer

can't do it that way either...my prof wants it done by the deﬁnition

anonymous · Answer

Oh, okay then, what you do here is expand F(x)^2, okay?
So, say f(x) = x+1
So, (x+1)^2 = x^2+2x+1

Then plug this into the limit definition, lim h-> 0 (f(x+h)-f(x))/h which will give your new g'(x)

anonymous · Answer

ok then how would I do it if it is$$g(x)= \sqrt[3]{f(x)}$$