Question

find dy/dx of y=(sin(x))^x

Answer 1

ln both sides

\[\ln y = x \ln (\sin x)\] do implicit differentiation yada yada...got it?

Answer 2

Yup. Makes sense. thanks.

Answer 3

so can you do it from here?

Answer 4

Yes I can... forgot about implicit. Should be good.

Answer 5

great :D

Answer 6

Phoenix, do you know why we use log differentiation here?

Answer 7

Phoenix, do you know why we use log differentiation here?

Answer 8

This would be helpful for the future.
\[d/dx (a^b) = 0\] because a and b are just constants.
\[d/dx (x^n) = nx^{n-1}\]
\[d/dx (f(x)^{g(x)}= \log differentiation\] because it's a function raised to a function.

Answer 9

n is a constant in the second case.

Answer 10

Thanks beeqay. Helpful to know that.