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Derivative of $$$\sqrt{a} \sin{\left(u \right)}$$$ with respect to $$$u$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{du} \left(\sqrt{a} \sin{\left(u \right)}\right)$$$.
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 $$$c = \sqrt{a}$$$ and $$$f{\left(u \right)} = \sin{\left(u \right)}$$$:
$${\color{red}\left(\frac{d}{du} \left(\sqrt{a} \sin{\left(u \right)}\right)\right)} = {\color{red}\left(\sqrt{a} \frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}$$The derivative of the sine is $$$\frac{d}{du} \left(\sin{\left(u \right)}\right) = \cos{\left(u \right)}$$$:
$$\sqrt{a} {\color{red}\left(\frac{d}{du} \left(\sin{\left(u \right)}\right)\right)} = \sqrt{a} {\color{red}\left(\cos{\left(u \right)}\right)}$$Thus, $$$\frac{d}{du} \left(\sqrt{a} \sin{\left(u \right)}\right) = \sqrt{a} \cos{\left(u \right)}$$$.
Answer
$$$\frac{d}{du} \left(\sqrt{a} \sin{\left(u \right)}\right) = \sqrt{a} \cos{\left(u \right)}$$$A