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