Find the Derivative - d/dx 16xe^x

Since ${\displaystyle 16}$ is constant with respect to ${\displaystyle x}$, the derivative of ${\displaystyle 16x{e}^x}$ with respect to ${\displaystyle x}$ is ${\displaystyle 16\frac{d}{dx}\left[x{e}^x\right]}$.

Differentiate using the Product Rule which states that ${\displaystyle \frac{d}{dx}\left[f\left(x\right)g\left(x\right)\right]}$ is ${\displaystyle f\left(x\right)\frac{d}{dx}\left[g\left(x\right)\right]+g\left(x\right)\frac{d}{dx}\left[f\left(x\right)\right]}$ where ${\displaystyle f\left(x\right)=x}$ and ${\displaystyle g\left(x\right)=e^x}$.

Differentiate using the Exponential Rule which states that ${\displaystyle \frac{d}{dx}\left[a^x\right]}$ is ${\displaystyle a^x\ln \left(a\right)}$ where ${\displaystyle a}$=${\displaystyle e}$.