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

1 Answer
Mar 5, 2018

Answer:

#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)#

.