Find the Derivative - d/d@VAR f(x)=cos( natural log of x)

Problem

d(cos(ln(x)))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule.

2. Apply the Chain Rule by differentiating the outer function cos(u) with respect to u where u=ln(x)

3. Differentiate the outer function, which results in −sin(ln(x))

4. Multiply by the derivative of the inner function ln(x) which is 1/x

5. Simplify the expression by combining the terms into a single fraction.

Final Answer

d(cos(ln(x)))/d(x)=−sin(ln(x))/x

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