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Derivative of $$$3 x z$$$ with respect to $$$z$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dz} \left(3 x z\right)$$$.
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 $$$c = 3 x$$$ and $$$f{\left(z \right)} = z$$$:
$${\color{red}\left(\frac{d}{dz} \left(3 x z\right)\right)} = {\color{red}\left(3 x \frac{d}{dz} \left(z\right)\right)}$$Apply the power rule $$$\frac{d}{dz} \left(z^{n}\right) = n z^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dz} \left(z\right) = 1$$$:
$$3 x {\color{red}\left(\frac{d}{dz} \left(z\right)\right)} = 3 x {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{dz} \left(3 x z\right) = 3 x$$$.
Answer
$$$\frac{d}{dz} \left(3 x z\right) = 3 x$$$A
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