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

Problem

d()/d(x)*cos(x)*sec(x)

Solution

1. Identify the trigonometric identity for the secant function, which is the reciprocal of the cosine function.

sec(x)=1/cos(x)

2. Substitute this identity into the original expression to simplify the function before differentiating.

cos(x)*sec(x)=cos(x)⋅1/cos(x)

3. Simplify the expression by canceling the common terms, assuming cos(x)≠0

cos(x)⋅1/cos(x)=1

4. Apply the constant rule for differentiation, which states that the derivative of any constant is zero.

d(1)/d(x)=0

Final Answer

(d(cos(x))*sec(x))/d(x)=0

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