klupko5HR

2022-11-25

What is the derivative of $xy$?

Expert

Rule for derivative products: $\frac{d\left(uv\right)}{dx}=u\frac{dv}{dx}+v\frac{du}{dx}$
Differentiate the function $xy$ with respect to $x$, we get
$\frac{d}{dx}\left(xy\right)=x\left(\frac{dy}{dx}\right)+y\left(\frac{dx}{dx}\right)$
$⇒$$\frac{d}{dx}\left(xy\right)=x\left(\frac{dy}{dx}\right)+y\left(1\right)$
$⇒$$\frac{d}{dx}\left(xy\right)=x\left(\frac{dy}{dx}\right)+y$
Hence, the derivative of $xy$ is $x\left(\frac{dy}{dx}\right)+y$.

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