Find the derivative of the function. $$ f(x)=e^{x}-x^{e} $$

Question

UpStudy AI · Accepted Answer

To find the derivative of the function $$ f(x) = e^{x} - x^{e} $$, we'll differentiate each term separately.

1. **Differentiate $$ e^{x} $$:**
   $$
   \frac{d}{dx} e^{x} = e^{x}
   $$

2. **Differentiate $$ x^{e} $$:**
   Since $$ e $$ is a constant, we use the power rule:
   $$
   \frac{d}{dx} x^{e} = e \cdot x^{e-1}
   $$

3. **Combine the results:**
   $$
   f'(x) = \frac{d}{dx} \left( e^{x} - x^{e} \right) = e^{x} - e \cdot x^{e-1}
   $$

**Final Answer:**
$$
f\,'(x) = e^{\,x} - e\,x^{\,e-1}
$$
The derivative of $$ f(x) = e^{x} - x^{e} $$ is $$ f\,'(x) = e^{x} - e \cdot x^{e-1} $$.

Find the derivative of the function. \[ f(x)=e^{x}-x^{e} \]