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

Problem

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

Solution

1. Identify the outer and inner functions to apply the Chain Rule. The outer function is tan(u) and the inner function is u=4*x

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

3. Differentiate the inner function with respect to x The derivative of 4*x is 4

4. Multiply the results together according to the Chain Rule formula.

5. Simplify the expression by placing the constant coefficient at the front.

Final Answer

d(tan(4*x))/d(x)=4*sec2(4*x)

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