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

Problem

d()/d(x)*(ex+xe)

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+xe)=d(ex)/d(x)+d(xe)/d(x)

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

d(ex)/d(x)=ex

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

d(xe)/d(x)=e*x(e−1)

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

d()/d(x)*(ex+xe)=ex+e*x(e−1)

Final Answer

d()/d(x)*(ex+xe)=ex+e*x(e−1)

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