What is the derivative of f(x)=5cos(3ln(x))?

Question

Please show work

Answer 1

f(x) = 5 cos(3ln(x))

start derivating the inner function.

Derivative of Logarithm Function is (d/dx)(logx) = 1/x

Derivative of Trigonometric Function is (d/dx)(cosx) = - sinx

Now we get that

f'(x) = 5 [- sin(3ln(x))] [3(1/x)]

 = - 5sin(3ln(x))][3/x]

Simplify

 = -(15/x)sin(3ln(x))