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Derivative of $$$6 u$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{du} \left(6 u\right)$$$.
Solution
Apply the constant multiple rule $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$ with $$$c = 6$$$ and $$$f{\left(u \right)} = u$$$:
$${\color{red}\left(\frac{d}{du} \left(6 u\right)\right)} = {\color{red}\left(6 \frac{d}{du} \left(u\right)\right)}$$Apply the power rule $$$\frac{d}{du} \left(u^{n}\right) = n u^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{du} \left(u\right) = 1$$$:
$$6 {\color{red}\left(\frac{d}{du} \left(u\right)\right)} = 6 {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{du} \left(6 u\right) = 6$$$.
Answer
$$$\frac{d}{du} \left(6 u\right) = 6$$$A
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