Question

Is this correct?

Answer 1

f(x) = x^y

Answer 2

ln(f(x)) = yln(x)

Answer 3

that's right!

Answer 4

taking the derivative of both sides
f'(x)/f(x) = y/x + ln(x)

Answer 5

f'(x) = f(x) * (y/x + ln(x))

Answer 6

f'(x) = (x^y)((y/x)+ln(x))

Answer 7

is y=y(x)?

Answer 8

oh

Answer 9

nvm

Answer 10

This is part of a larger question, but I got it now.

Answer 11

I think, that:
\[\frac{ f'(x) }{ f(x) }=y'(x)\ln y+\frac{ y }{ x }\]

Answer 12

so:
\[f'(x)=f(x)[y'(x)\ln x+\frac{ y }{ x }]\]