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

Problem

d()/d(x)*(−csc(x)−sin(x))

Solution

1. Identify the function to be differentiated, which is y=−csc(x)−sin(x) Note that the task asks for the derivative of y with respect to x

2. Apply the sum rule for derivatives, which allows for the differentiation of each term individually.

d(y)/d(x)=(d(−)*csc(x))/d(x)+(d(−)*sin(x))/d(x)

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

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

4. Apply the derivative rule for the sine function, where d(sin(x))/d(x)=cos(x)

(d(−)*sin(x))/d(x)=−cos(x)

5. Combine the results to find the final derivative expression.

d(y)/d(x)=csc(x)*cot(x)−cos(x)

Final Answer

d(y)/d(x)=csc(x)*cot(x)−cos(x)

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