Derivative of $$$\pi n y$$$ with respect to $$$y$$$
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Your Input
Find $$$\frac{d}{dy} \left(\pi n y\right)$$$.
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 $$$c = \pi n$$$ and $$$f{\left(y \right)} = y$$$:
$${\color{red}\left(\frac{d}{dy} \left(\pi n y\right)\right)} = {\color{red}\left(\pi n \frac{d}{dy} \left(y\right)\right)}$$Apply the power rule $$$\frac{d}{dy} \left(y^{m}\right) = m y^{m - 1}$$$ with $$$m = 1$$$, in other words, $$$\frac{d}{dy} \left(y\right) = 1$$$:
$$\pi n {\color{red}\left(\frac{d}{dy} \left(y\right)\right)} = \pi n {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{dy} \left(\pi n y\right) = \pi n$$$.
Answer
$$$\frac{d}{dy} \left(\pi n y\right) = \pi n$$$A