Find the Derivative - d/dx f(x)=tan(2x)

Problem

d(tan(2*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=2*x

2. Apply the derivative of the outer function. The derivative of tan(u) with respect to u is sec2(u)

3. Apply the Chain Rule by multiplying the derivative of the outer function by the derivative of the inner function, (d(2)*x)/d(x)

4. Differentiate the inner function. The derivative of 2*x is 2

5. Combine the results to find the final derivative.

Final Answer

d(tan(2*x))/d(x)=2*sec2(2*x)

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