Find the Derivative - d/dx sec(1/x)

Problem

d(sec(1/x))/d(x)

Solution

1. Identify the outer function as sec(u) and the inner function as u=1/x

2. Apply the chain rule, which states that d(ƒ(u))/d(x)=d(ƒ)/d(u)⋅d(u)/d(x)

3. Differentiate the outer function sec(u) with respect to u to get sec(u)*tan(u)

4. Differentiate the inner function u=x(−1) with respect to x to get −x(−2) which is −1/(x2)

5. Multiply the results of the derivatives together.

6. Substitute u=1/x back into the expression.

Final Answer

d(sec(1/x))/d(x)=−(sec(1/x)*tan(1/x))/(x2)

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