Find the Derivative - d/dx e^x-cot(x)

Problem

d()/d(x)*(e^x−cot(x))

Solution

1. Apply the sum/difference rule for derivatives, which allows the derivative of a sum or difference to be calculated as the sum or difference of the individual derivatives.

d()/d(x)*(e^x−cot(x))=d(e^x)/d(x)−d(cot(x))/d(x)

2. Differentiate the exponential term using the rule that the derivative of e^x is itself.

d(e^x)/d(x)=e^x

3. Differentiate the trigonometric term using the standard derivative rule for the cotangent function.

d(cot(x))/d(x)=−csc^2(x)

4. Combine the results and simplify the signs.

e^x−(−csc^2(x))=e^x+csc^2(x)

Final Answer

d()/d(x)*(e^x−cot(x))=e^x+csc^2(x)

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