Derivative of $$$x y^{2}$$$ with respect to $$$x$$$
The calculator will find the derivative of $$$x y^{2}$$$ with respect to $$$x$$$, with steps shown.
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Your Input
Find $$$\frac{d}{dx} \left(x y^{2}\right)$$$.
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 $$$c = y^{2}$$$ and $$$f{\left(x \right)} = x$$$:
$${\color{red}\left(\frac{d}{dx} \left(x y^{2}\right)\right)} = {\color{red}\left(y^{2} \frac{d}{dx} \left(x\right)\right)}$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dx} \left(x\right) = 1$$$:
$$y^{2} {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = y^{2} {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{dx} \left(x y^{2}\right) = y^{2}$$$.
Answer
$$$\frac{d}{dx} \left(x y^{2}\right) = y^{2}$$$A