Find the Derivative - d/dx x^e

Problem

d(xe)/d(x)

Solution

1. Identify the type of function being differentiated. Since the base is the variable x and the exponent is a constant e this is a power function.

2. Apply the power rule for derivatives, which states that d(xn)/d(x)=n*x(n−1) for any constant n

3. Substitute n=e into the power rule formula.

4. Simplify the expression by writing the constant coefficient in front of the variable.

Final Answer

d(xe)/d(x)=e*x(e−1)

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