Find the Derivative - d/dx tan(8x)

Problem

d(tan(8*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=8*x

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

3. Differentiate the inner function with respect to x The derivative of 8*x is 8

4. Apply the Chain Rule by multiplying the derivative of the outer function by the derivative of the inner function.

d(tan(8*x))/d(x)=sec2(8*x)⋅8

5. Simplify the expression by moving the constant factor to the front.

Final Answer

d(tan(8*x))/d(x)=8*sec2(8*x)

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