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

Problem

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

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

2. Differentiate the exponential function e^x The derivative of e^x with respect to x is simply e^x

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

3. Apply the power rule to the term x^e Since e is a constant, the derivative of x^n is n*x^(n−1)

d(x^e)/d(x)=e*x^(e−1)

4. Combine the results to find the final derivative of the expression.

d()/d(x)*(e^x+x^e)=e^x+e*x^(e−1)

Final Answer

d()/d(x)*(e^x+x^e)=e^x+e*x^(e−1)

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