Question

How do you find the derivative of the function `f(w) = ln(sin(w−15))`?

Answer 1

`cot(w-15))`

Explanation:

this is just by using the Chain rule
https://en.wikipedia.org/wiki/Chain_rule

the derivative of the inside function `sin(w-15)` is `cos(w-15)`
and the derivative of the outside function `d/dx ln(x) = 1/x`

therefore, the derivative of this whole is the derivative of the outside function evaluated at the inside function multiplied by the derivative of the inside function
that is,
`d/dx f(g(x)) = f'(g(x))*g'(x)`

that is equal to
`1/sin(w-15) * cos(w-15)`

which is
`cos(w-15)/sin(w-15)`

and that is equal to

`cot(w-15)`

.