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

Problem

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

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

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

3. Differentiate the second term using the chain rule, where the derivative of e^u is e^u⋅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.

e^x−e^(−x)

Final Answer

d()/d(x)*(e^x+e^(−x))=e^x−e^(−x)

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