Find the Derivative - d/dx sec(x^2)

Problem

d(sec(x2))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is sec(u) and the inner function is u=x2

2. Apply the Chain Rule by differentiating the outer function with respect to u and then multiplying by the derivative of the inner function.

3. Differentiate the outer function sec(u) which results in sec(u)*tan(u)

4. Differentiate the inner function x2 using the Power Rule, which results in 2*x

5. Substitute u=x2 back into the expression and combine the terms.

Final Answer

d(sec(x2))/d(x)=2*x*sec(x2)*tan(x2)

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