|
Derivative of $$$y z^{2}$$$ with respect to $$$z$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dz} \left(y z^{2}\right)$$$.
Solution
Apply the constant multiple rule $$$\frac{d}{dz} \left(c f{\left(z \right)}\right) = c \frac{d}{dz} \left(f{\left(z \right)}\right)$$$ with $$$c = y$$$ and $$$f{\left(z \right)} = z^{2}$$$:
$${\color{red}\left(\frac{d}{dz} \left(y z^{2}\right)\right)} = {\color{red}\left(y \frac{d}{dz} \left(z^{2}\right)\right)}$$Apply the power rule $$$\frac{d}{dz} \left(z^{n}\right) = n z^{n - 1}$$$ with $$$n = 2$$$:
$$y {\color{red}\left(\frac{d}{dz} \left(z^{2}\right)\right)} = y {\color{red}\left(2 z\right)}$$Thus, $$$\frac{d}{dz} \left(y z^{2}\right) = 2 y z$$$.
Answer
$$$\frac{d}{dz} \left(y z^{2}\right) = 2 y z$$$A