Find the Derivative - d/dx tan(x)^3

Problem

d(tan3(x))/d(x)

Solution

1. Identify the outer and inner functions to apply the power rule and the chain rule. The expression is (tan(x))3

2. Apply the power rule to the outer function u3 which gives 3*u2

3. Apply the chain rule by multiplying by the derivative of the inner function, tan(x)

4. Recall the derivative of tan(x) which is sec2(x)

5. Combine the results to find the final derivative.

Final Answer

d(tan3(x))/d(x)=3*tan2(x)*sec2(x)

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