How do you find the derivative of the function f(w) = ln(sin(w−15))f(w)=ln(sin(w15))?

1 Answer
Mar 5, 2018

cot(w-15))cot(w15))

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)sin(w15) is cos(w-15)cos(w15)
and the derivative of the outside function d/dx ln(x) = 1/xddxln(x)=1x

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)

.