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Derivative of $$$x^{2} y$$$ with respect to $$$x$$$
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Your Input
Find $$$\frac{d}{dx} \left(x^{2} y\right)$$$.
Solution
Apply the constant multiple rule $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$ with $$$c = y$$$ and $$$f{\left(x \right)} = x^{2}$$$:
$${\color{red}\left(\frac{d}{dx} \left(x^{2} y\right)\right)} = {\color{red}\left(y \frac{d}{dx} \left(x^{2}\right)\right)}$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 2$$$:
$$y {\color{red}\left(\frac{d}{dx} \left(x^{2}\right)\right)} = y {\color{red}\left(2 x\right)}$$Thus, $$$\frac{d}{dx} \left(x^{2} y\right) = 2 x y$$$.
Answer
$$$\frac{d}{dx} \left(x^{2} y\right) = 2 x y$$$A