## PhoenixFire find dy/dx of y=(sin(x))^x one year ago one year ago

1. lgbasallote

ln both sides $\ln y = x \ln (\sin x)$ do implicit differentiation yada yada...got it?

2. PhoenixFire

Yup. Makes sense. thanks.

3. lgbasallote

so can you do it from here?

4. PhoenixFire

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

5. lgbasallote

great :D

6. beeqay

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

7. beeqay

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

8. beeqay

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.

9. beeqay

n is a constant in the second case.

10. PhoenixFire

Thanks beeqay. Helpful to know that.