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

Problem

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

Solution

1. Simplify the expression using trigonometric identities. Recall that the reciprocal of the secant function is the cosine function.

1/sec(x)=cos(x)

2. Apply the derivative rule for the cosine function. The derivative of cos(x) with respect to x is −sin(x)

d(cos(x))/d(x)=−sin(x)

Final Answer

d()/d(x)1/sec(x)=−sin(x)

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