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

Problem

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

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

d(tan(u))/d(u)=sec2(u)

3. Differentiate the inner function with respect to x The derivative of x/2 is 1/2

d()/d(x)x/2=1/2

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

d(tan(x/2))/d(x)=sec2(x/2)⋅1/2

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

d(tan(x/2))/d(x)=1/2*sec2(x/2)

Final Answer

d(tan(x/2))/d(x)=1/2*sec2(x/2)

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