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

Problem

d()/d(x)*(−csc(x)−cos(x))

Solution

1. Apply the sum rule for differentiation, which allows the derivative of a sum or difference to be taken term by term.

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

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

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

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

−(−csc(x)*cot(x))−d(cos(x))/d(x)

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

csc(x)*cot(x)−(−sin(x))

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

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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