Find the Derivative - d/dx sin(9 natural log of x)

Problem

d(sin(9*ln(x)))/d(x)

Solution

1. Identify the outer and inner functions to apply the chain rule. The outer function is sin(u) and the inner function is u=9*ln(x)

2. Apply the chain rule by differentiating the outer function with respect to the inner function.

d(sin(u))/d(u)=cos(u)

3. Differentiate the inner function 9*ln(x) with respect to x

(d(9)*ln(x))/d(x)=9⋅1/x

4. Combine the results using the chain rule formula d(y)/d(x)=d(y)/d(u)⋅d(u)/d(x)

cos(9*ln(x))⋅9/x

5. Simplify the expression into a single fraction.

(9*cos(9*ln(x)))/x

Final Answer

d(sin(9*ln(x)))/d(x)=(9*cos(9*ln(x)))/x

Want more problems? Check here!