## PhoenixFire Group Title find dy/dx of y=(sin(x))^x 2 years ago 2 years ago

1. lgbasallote Group Title

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

2. PhoenixFire Group Title

Yup. Makes sense. thanks.

3. lgbasallote Group Title

so can you do it from here?

4. PhoenixFire Group Title

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

5. lgbasallote Group Title

great :D

6. beeqay Group Title

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

7. beeqay Group Title

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

8. beeqay Group Title

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 Group Title

n is a constant in the second case.

10. PhoenixFire Group Title

Thanks beeqay. Helpful to know that.