Chapter 11 - Section 11.5 - Derivatives of Logarithmic and Exponential Functions - Exercises - Page 842: 45

$f^{\prime}(x)=e^{x}(1+x)$

With $u(x)=x, \quad v(x)=e^{x},$ $f(x)=u(x)\cdot v(x),$ so we use the product rule: $f^{\prime}(x)=u(x)^{\prime}\cdot v(x)+u(x)\cdot v^{\prime}(x)$ $=(1)e^{x}+x(e^{x})$ $f^{\prime}(x)=e^{x}(1+x)$