Find the Derivative - d/dx 2csc(x)+5cos(x)

Problem

d()/d(x)*(2*csc(x)+5*cos(x))

Solution

1. Apply the sum rule for derivatives, which allows the differentiation of each term independently.

d()/d(x)*(2*csc(x)+5*cos(x))=(d(2)*csc(x))/d(x)+(d(5)*cos(x))/d(x)

2. Apply the constant multiple rule to move the coefficients outside of the derivatives.

2d(csc(x))/d(x)+5d(cos(x))/d(x)

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

2*(−csc(x)*cot(x))+5d(cos(x))/d(x)

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

2*(−csc(x)*cot(x))+5*(−sin(x))

5. Simplify the expression by multiplying the constants through the terms.

−2*csc(x)*cot(x)−5*sin(x)

Final Answer

d()/d(x)*(2*csc(x)+5*cos(x))=−2*csc(x)*cot(x)−5*sin(x)

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