Here's the question you clicked on:
PhoenixFire
find dy/dx of y=(sin(x))^x
ln both sides \[\ln y = x \ln (\sin x)\] do implicit differentiation yada yada...got it?
Yup. Makes sense. thanks.
so can you do it from here?
Yes I can... forgot about implicit. Should be good.
Phoenix, do you know why we use log differentiation here?
Phoenix, do you know why we use log differentiation here?
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.
n is a constant in the second case.
Thanks beeqay. Helpful to know that.