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

Problem

d()/d(x)*(e−e^x+x^e)

Solution

1. Apply the sum and difference rule for derivatives to differentiate each term individually.

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

2. Differentiate the constant e Since e is a constant approximately equal to 2.718 its derivative with respect to x is zero.

d(e)/d(x)=0

3. 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

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

d(x^e)/d(x)=e*x^(e−1)

5. Combine the results to find the final derivative expression.

0−e^x+e*x^(e−1)

Final Answer

d()/d(x)*(e−e^x+x^e)=e*x^(e−1)−e^x

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