Find the Derivative - d/d@VAR f(x)=( natural log of x)^3

Problem

d()/d(x)*(ln(x))3

Solution

1. Identify the outer and inner functions to apply the chain rule. The outer function is u3 and the inner function is u=ln(x)

2. Apply the power rule to the outer function, which gives 3*u2

3. Apply the chain rule by multiplying the derivative of the outer function by the derivative of the inner function, d(ln(x))/d(x)

4. Substitute the derivative of the inner function, which is 1/x

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

Final Answer

d()/d(x)*(ln(x))3=(3*(ln(x))2)/x

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