Question

f(x) = [ln x ]^(7)
find f'(x) and f'(e^4)

Answer 1

Remember to use the chain rule

Answer 2

this is the chain rule

let u = ln(x) u' = 1/x

y = u^7 y' = 7u^6

the

f'(x) = 7(ln(x))^6 * 1/x

Answer 3

oh ok does it matter which one if u and v

Answer 4

No he just used it to make it look more simple and less intimidating

Answer 5

It can easily be done without doing a u substitution

Answer 6

then substitute x = e^4

Answer 7

is this what im suppose to get 28672/e^4

Answer 8

well I would have thought you would have gotten

\[\frac{7 \times((\ln(e^4))^6}{e^4} = \frac{7 \times 4^6}{e^4} = \frac{7 \times 4096}{e^4}\]

which gives the answer you have.