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