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

Problem

d(sec2(x))/d(x)

Solution

1. Identify the function as a composition of functions where the outer function is u2 and the inner function is sec(x)

2. Apply the power rule to the outer function, which gives 2*sec(x)

3. Apply the chain rule by multiplying by the derivative of the inner function, d(sec(x))/d(x)

4. Substitute the known derivative d(sec(x))/d(x)=sec(x)*tan(x)

5. Simplify the resulting expression by combining the sec(x) terms.

Final Answer

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

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