Question

I need help finding the derivative of this function:

f(x)=(X^2+2)^4/5

Thanks in advance! Any help would be greatly appreciated!

Answer 1

just use the chain rule

f'(x) = (4/5) (x^2+2)^(-1/5) (2x)
= ...

Answer 2

You break it into parts to turn it into a simpler equation so:

set u= x^2 + 2
then your equation becomes:
f(u)= u^4/5
and f'(x) = f'(u)* u'

f'(u) = 4/5 * u^(4/5-1) = 4/5 * u^-1/5

Now take the derivative of u to get
u' = 2x

Then substitute to get in terms of x
f'(x) =4/5 * (x^2 + 2)^-1/5 * 2x