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

Problem

d()/d(x)sec(x)/tan(x)

Solution

1. Simplify the expression using trigonometric identities before differentiating.

2. Substitute the definitions sec(x)=1/cos(x) and tan(x)=sin(x)/cos(x) into the fraction.

sec(x)/tan(x)=1/cos(x)/sin(x)/cos(x)

3. Cancel the common denominator cos(x) from the numerator and denominator.

1/cos(x)⋅cos(x)/sin(x)=1/sin(x)

4. Identify the reciprocal identity 1/sin(x)=csc(x)

5. Differentiate the simplified function csc(x) with respect to x

d(csc(x))/d(x)=−csc(x)*cot(x)

Final Answer

d()/d(x)sec(x)/tan(x)=−csc(x)*cot(x)

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