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

Problem

d()/d(x)*csc2(x)

Solution

1. Identify the function as a composition of functions where the outer function is u2 and the inner function is csc(x)

2. Apply the power rule to the outer function, which gives 2*csc(x)

3. Apply the chain rule by multiplying by the derivative of the inner function, d(csc(x))/d(x)

4. Substitute the known derivative d(csc(x))/d(x)=−csc(x)*cot(x)

5. Multiply the terms together to simplify the expression.

2*csc(x)⋅(−csc(x)*cot(x))

−2*csc2(x)*cot(x)

Final Answer

d(csc2(x))/d(x)=−2*csc2(x)*cot(x)

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