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

Problem

d()/d(x)*(ex+e(−x))

Solution

1. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives.

d()/d(x)*(ex+e(−x))=d(ex)/d(x)+d(e(−x))/d(x)

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

d(ex)/d(x)=ex

3. Differentiate the second term using the chain rule, where the derivative of eu is eu⋅d(u)/d(x)

d(e(−x))/d(x)=e(−x)⋅d(−x)/d(x)

4. Calculate the derivative of the exponent −x which is −1

d(e(−x))/d(x)=e(−x)⋅(−1)=−e(−x)

5. Combine the results to find the final derivative.

ex−e(−x)

Final Answer

d()/d(x)*(ex+e(−x))=ex−e(−x)

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