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

Answer 1

by the chain rule
\[g'(x)=2f(x)f'(x)\]

Answer 2

I can't use the chain rule yet on it

Answer 3

Then use the product rule: So \[g'(x)=f(x)f'(x)+f'(x)f(x)\]

Answer 4

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

Answer 5

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)

Answer 6

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