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Derivative of $$$- 5 y$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dy} \left(- 5 y\right)$$$.
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 $$$c = -5$$$ and $$$f{\left(y \right)} = y$$$:
$${\color{red}\left(\frac{d}{dy} \left(- 5 y\right)\right)} = {\color{red}\left(- 5 \frac{d}{dy} \left(y\right)\right)}$$Apply the power rule $$$\frac{d}{dy} \left(y^{n}\right) = n y^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dy} \left(y\right) = 1$$$:
$$- 5 {\color{red}\left(\frac{d}{dy} \left(y\right)\right)} = - 5 {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{dy} \left(- 5 y\right) = -5$$$.
Answer
$$$\frac{d}{dy} \left(- 5 y\right) = -5$$$A
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