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

Problem

d()/d(x)*(−csc(x)−cos(x))

Solution

1. Apply the sum rule for differentiation, which allows for the derivative of each term to be taken individually.

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

2. Factor out constants from each term to simplify the differentiation process.

d(y)/d(x)=−d(csc(x))/d(x)−d(cos(x))/d(x)

3. Differentiate the cosecant function using the standard trigonometric derivative rule d(csc(x))/d(x)=−csc(x)*cot(x)

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

4. Differentiate the cosine function using the standard trigonometric derivative rule d(cos(x))/d(x)=−sin(x)

d(y)/d(x)=csc(x)*cot(x)−(−sin(x))

5. Simplify the signs to arrive at the final expression for the derivative.

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

Final Answer

d()/d(x)*(−csc(x)−cos(x))=csc(x)*cot(x)+sin(x)

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