Derivative of $$$6 - \frac{a}{50}$$$
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Find $$$\frac{d}{da} \left(6 - \frac{a}{50}\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{da} \left(6 - \frac{a}{50}\right)\right)} = {\color{red}\left(\frac{d}{da} \left(6\right) - \frac{d}{da} \left(\frac{a}{50}\right)\right)}$$Apply the constant multiple rule $$$\frac{d}{da} \left(c f{\left(a \right)}\right) = c \frac{d}{da} \left(f{\left(a \right)}\right)$$$ with $$$c = \frac{1}{50}$$$ and $$$f{\left(a \right)} = a$$$:
$$- {\color{red}\left(\frac{d}{da} \left(\frac{a}{50}\right)\right)} + \frac{d}{da} \left(6\right) = - {\color{red}\left(\frac{\frac{d}{da} \left(a\right)}{50}\right)} + \frac{d}{da} \left(6\right)$$Apply the power rule $$$\frac{d}{da} \left(a^{n}\right) = n a^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{da} \left(a\right) = 1$$$:
$$- \frac{{\color{red}\left(\frac{d}{da} \left(a\right)\right)}}{50} + \frac{d}{da} \left(6\right) = - \frac{{\color{red}\left(1\right)}}{50} + \frac{d}{da} \left(6\right)$$The derivative of a constant is $$$0$$$:
$${\color{red}\left(\frac{d}{da} \left(6\right)\right)} - \frac{1}{50} = {\color{red}\left(0\right)} - \frac{1}{50}$$Thus, $$$\frac{d}{da} \left(6 - \frac{a}{50}\right) = - \frac{1}{50}$$$.
Answer
$$$\frac{d}{da} \left(6 - \frac{a}{50}\right) = - \frac{1}{50}$$$A