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

Problem

d()/d(x)1/tan(x)

Solution

1. Identify the expression as the cotangent function using the trigonometric identity cot(x)=1/tan(x)

2. Rewrite the derivative problem in terms of the cotangent function.

d()/d(x)*cot(x)

3. Apply the derivative rule for the cotangent function, which states that d(cot(x))/d(x)=−csc2(x)

4. Simplify the result if necessary, noting that the derivative is expressed in terms of the cosecant function.

Final Answer

d()/d(x)1/tan(x)=−csc2(x)

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