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

Problem

d(tan^3(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 u^3 which gives 3*u^2

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 sec^2(x)

5. Combine the results to find the final derivative.

Final Answer

d(tan^3(x))/d(x)=3*tan^2(x)*sec^2(x)

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