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Derivative of $$$1 - y$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dy} \left(1 - y\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dy} \left(1 - y\right)\right)} = {\color{red}\left(\frac{d}{dy} \left(1\right) - \frac{d}{dy} \left(y\right)\right)}$$Apply the power rule $$$\frac{d}{dy} \left(y^{n}\right) = n y^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dy} \left(y\right) = 1$$$:
$$- {\color{red}\left(\frac{d}{dy} \left(y\right)\right)} + \frac{d}{dy} \left(1\right) = - {\color{red}\left(1\right)} + \frac{d}{dy} \left(1\right)$$The derivative of a constant is $$$0$$$:
$${\color{red}\left(\frac{d}{dy} \left(1\right)\right)} - 1 = {\color{red}\left(0\right)} - 1$$Thus, $$$\frac{d}{dy} \left(1 - y\right) = -1$$$.
Answer
$$$\frac{d}{dy} \left(1 - y\right) = -1$$$A
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