Question

What is the derivative of $xy$?

Answer 1

Derivative product rule: $\frac{d\left(uv\right)}{dx}=u\frac{dv}{dx}+v\frac{du}{dx}$

Differentiate the function $xy$ with respect to $x$, we get

$\frac{d}{dx}\left(xy\right)=x\left(\frac{dy}{dx}\right)+y\left(\frac{dx}{dx}\right)$

$\Rightarrow$$\frac{d}{dx}\left(xy\right)=x\left(\frac{dy}{dx}\right)+y\left(1\right)$

$\Rightarrow$$\frac{d}{dx}\left(xy\right)=x\left(\frac{dy}{dx}\right)+y$

Hence, the derivative of $xy$ is $x\left(\frac{dy}{dx}\right)+y$.