Find the Derivative - d/dx tan(x)^4

Problem

d(tan(x))/d(x)

Solution

1. Identify the outer and inner functions to apply the Power Rule and the Chain Rule. The expression is of the form un where u=tan(x) and n=4

2. Apply the Power Rule by bringing the exponent to the front and subtracting one from the exponent.

d(tan(x))/d(x)=4*tan(x)⋅d(tan(x))/d(x)

3. Differentiate the inner function tan(x) using the trigonometric derivative rule d(tan(x))/d(x)=sec(x)

d(tan(x))/d(x)=4*tan(x)*sec(x)

Final Answer

d(tan(x))/d(x)=4*tan(x)*sec(x)

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