Derivative of $$$- y^{2}$$$
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Your Input
Find $$$\frac{d}{dy} \left(- y^{2}\right)$$$.
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 $$$c = -1$$$ and $$$f{\left(y \right)} = y^{2}$$$:
$${\color{red}\left(\frac{d}{dy} \left(- y^{2}\right)\right)} = {\color{red}\left(- \frac{d}{dy} \left(y^{2}\right)\right)}$$Apply the power rule $$$\frac{d}{dy} \left(y^{n}\right) = n y^{n - 1}$$$ with $$$n = 2$$$:
$$- {\color{red}\left(\frac{d}{dy} \left(y^{2}\right)\right)} = - {\color{red}\left(2 y\right)}$$Thus, $$$\frac{d}{dy} \left(- y^{2}\right) = - 2 y$$$.
Answer
$$$\frac{d}{dy} \left(- y^{2}\right) = - 2 y$$$A