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

Problem

d()/d(x)*(e−ex+xe)

Solution

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

d()/d(x)*(e−ex+xe)=d(e)/d(x)−d(ex)/d(x)+d(xe)/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 ex The derivative of ex with respect to x is simply ex

d(ex)/d(x)=ex

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

d(xe)/d(x)=e*x(e−1)

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

0−ex+e*x(e−1)

Final Answer

d()/d(x)*(e−ex+xe)=e*x(e−1)−ex

Want more problems? Check here!