# Find the Derivative f(x)=sin(5 natural log of x)

Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
The derivative of with respect to is .
Replace all occurrences of with .
Differentiate using the Constant Multiple Rule.
Since is constant with respect to , the derivative of with respect to is .
Move to the left of .
The derivative of with respect to is .
Combine fractions.
Combine and .
Combine and .
Simplify by moving inside the logarithm.
Find the Derivative f(x)=sin(5 natural log of x)