Derivative of $$$- a + b$$$ with respect to $$$a$$$
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Your Input
Find $$$\frac{d}{da} \left(- a + b\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{da} \left(- a + b\right)\right)} = {\color{red}\left(- \frac{d}{da} \left(a\right) + \frac{db}{da}\right)}$$The derivative of a constant is $$$0$$$:
$${\color{red}\left(\frac{db}{da}\right)} - \frac{d}{da} \left(a\right) = {\color{red}\left(0\right)} - \frac{d}{da} \left(a\right)$$Apply the power rule $$$\frac{d}{da} \left(a^{n}\right) = n a^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{da} \left(a\right) = 1$$$:
$$- {\color{red}\left(\frac{d}{da} \left(a\right)\right)} = - {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{da} \left(- a + b\right) = -1$$$.
Answer
$$$\frac{d}{da} \left(- a + b\right) = -1$$$A
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