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