Find the Derivative - d/dx cot(x)^2

Problem

d(cot2(x))/d(x)

Solution

1. Identify the outer and inner functions to apply the power rule and the chain rule, where the expression is (cot(x))2

2. Apply the power rule by bringing the exponent 2 to the front and decreasing the power by 1

d(cot2(x))/d(x)=2*cot(x)⋅d(cot(x))/d(x)

3. Apply the derivative rule for the inner function, where d(cot(x))/d(x)=−csc2(x)

d(cot2(x))/d(x)=2*cot(x)⋅(−csc2(x))

4. Simplify the expression by multiplying the terms together.

d(cot2(x))/d(x)=−2*cot(x)*csc2(x)

Final Answer

d(cot2(x))/d(x)=−2*cot(x)*csc2(x)

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