|
Derivative of $$$x y z$$$ with respect to $$$y$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dy} \left(x y z\right)$$$.
Solution
Apply the constant multiple rule $$$\frac{d}{dy} \left(c f{\left(y \right)}\right) = c \frac{d}{dy} \left(f{\left(y \right)}\right)$$$ with $$$c = x z$$$ and $$$f{\left(y \right)} = y$$$:
$${\color{red}\left(\frac{d}{dy} \left(x y z\right)\right)} = {\color{red}\left(x z \frac{d}{dy} \left(y\right)\right)}$$Apply the power rule $$$\frac{d}{dy} \left(y^{n}\right) = n y^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dy} \left(y\right) = 1$$$:
$$x z {\color{red}\left(\frac{d}{dy} \left(y\right)\right)} = x z {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{dy} \left(x y z\right) = x z$$$.
Answer
$$$\frac{d}{dy} \left(x y z\right) = x z$$$A