Derivative of $$$\frac{\sqrt{6} \sin{\left(v \right)}}{6}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dv} \left(\frac{\sqrt{6} \sin{\left(v \right)}}{6}\right)$$$.
Solution
Apply the constant multiple rule $$$\frac{d}{dv} \left(c f{\left(v \right)}\right) = c \frac{d}{dv} \left(f{\left(v \right)}\right)$$$ with $$$c = \frac{\sqrt{6}}{6}$$$ and $$$f{\left(v \right)} = \sin{\left(v \right)}$$$:
$${\color{red}\left(\frac{d}{dv} \left(\frac{\sqrt{6} \sin{\left(v \right)}}{6}\right)\right)} = {\color{red}\left(\frac{\sqrt{6}}{6} \frac{d}{dv} \left(\sin{\left(v \right)}\right)\right)}$$The derivative of the sine is $$$\frac{d}{dv} \left(\sin{\left(v \right)}\right) = \cos{\left(v \right)}$$$:
$$\frac{\sqrt{6} {\color{red}\left(\frac{d}{dv} \left(\sin{\left(v \right)}\right)\right)}}{6} = \frac{\sqrt{6} {\color{red}\left(\cos{\left(v \right)}\right)}}{6}$$Thus, $$$\frac{d}{dv} \left(\frac{\sqrt{6} \sin{\left(v \right)}}{6}\right) = \frac{\sqrt{6} \cos{\left(v \right)}}{6}$$$.
Answer
$$$\frac{d}{dv} \left(\frac{\sqrt{6} \sin{\left(v \right)}}{6}\right) = \frac{\sqrt{6} \cos{\left(v \right)}}{6}$$$A