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

Problem

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

2. Differentiate the exponential term using the rule that the derivative of ex is itself.

d(ex)/d(x)=ex

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

d(cot(x))/d(x)=−csc2(x)

4. Combine the results and simplify the signs.

ex−(−csc2(x))=ex+csc2(x)

Final Answer

d()/d(x)*(ex−cot(x))=ex+csc2(x)

Want more problems? Check here!