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

Problem

(d(−)*csc(x))/d(x)

Solution

1. Identify the function as a composition of functions where the outer function is the square and the inner function is −csc(x)

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

(d(−)*csc(x))/d(x)=−2*csc(x)⋅d(csc(x))/d(x)

3. Apply the derivative rule for the cosecant function, which is d(csc(x))/d(x)=−csc(x)*cot(x)

(d(−)*csc(x))/d(x)=−2*csc(x)*(−csc(x)*cot(x))

4. Simplify the expression by multiplying the terms and combining the signs.

(d(−)*csc(x))/d(x)=2*csc(x)*cot(x)

Final Answer

(d(−)*csc(x))/d(x)=2*csc(x)*cot(x)

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