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

Problem

d(csc(x))/d(x)

Solution

1. Identify the function to be differentiated, which is the cosecant function y=csc(x)

2. Rewrite the cosecant function in terms of the sine function using the reciprocal identity csc(x)=1/sin(x)

3. Apply the quotient rule or the power rule combined with the chain rule to the expression (sin(x))(−1)

4. Differentiate the expression to get −(sin(x))(−2)⋅cos(x)

5. Simplify the resulting expression by separating the terms into −1/sin(x)⋅cos(x)/sin(x)

6. Substitute the trigonometric identities csc(x)=1/sin(x) and cot(x)=cos(x)/sin(x) back into the expression.

Final Answer

d(csc(x))/d(x)=−csc(x)*cot(x)

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