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

Problem

d(cot(sin(x)))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Power Rule. The expression is of the form u2 where u=cot(sin(x))

2. Apply the Power Rule by bringing the exponent to the front and decreasing the power by one.

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

3. Apply the Chain Rule to the derivative of the cotangent function. The derivative of cot(u) is −csc2(u)

d(cot(sin(x)))/d(x)=−csc2(sin(x))⋅d(sin(x))/d(x)

4. Differentiate the innermost function sin(x) which results in cos(x)

d(sin(x))/d(x)=cos(x)

5. Combine all the components obtained from the chain rule steps.

d(cot(sin(x)))/d(x)=2*cot(sin(x))⋅(−csc2(sin(x)))⋅cos(x)

6. Simplify the expression by rearranging the terms and signs.

d(cot(sin(x)))/d(x)=−2*cos(x)*cot(sin(x))*csc2(sin(x))

Final Answer

d(cot(sin(x)))/d(x)=−2*cos(x)*cot(sin(x))*csc2(sin(x))

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