Find the Derivative - d/dx tan(5x)

Problem

d(tan(5*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=5*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 5*x is 5

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

d(tan(5*x))/d(x)=sec2(5*x)⋅5

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

d(tan(5*x))/d(x)=5*sec2(5*x)

Final Answer

d(tan(5*x))/d(x)=5*sec2(5*x)

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