Find the Derivative - d/dx tan(pix)

Problem

d(tan(π*x))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is tan(u) and the inner function is u=π*x

2. Apply the derivative of the tangent function, which is sec2(u)

3. Differentiate the inner function π*x with respect to x which results in the constant π

4. Multiply the derivative of the outer function by the derivative of the inner function according to the Chain Rule.

d(tan(π*x))/d(x)=sec2(π*x)⋅(d(π)*x)/d(x)

d(tan(π*x))/d(x)=sec2(π*x)⋅π

Final Answer

d(tan(π*x))/d(x)=π*sec2(π*x)

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