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Derivative of $$$32 y$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dy} \left(32 y\right)$$$.
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 $$$c = 32$$$ and $$$f{\left(y \right)} = y$$$:
$${\color{red}\left(\frac{d}{dy} \left(32 y\right)\right)} = {\color{red}\left(32 \frac{d}{dy} \left(y\right)\right)}$$Apply the power rule $$$\frac{d}{dy} \left(y^{n}\right) = n y^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dy} \left(y\right) = 1$$$:
$$32 {\color{red}\left(\frac{d}{dy} \left(y\right)\right)} = 32 {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{dy} \left(32 y\right) = 32$$$.
Answer
$$$\frac{d}{dy} \left(32 y\right) = 32$$$A
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