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Derivative of $$$\frac{\sqrt{7} \sin{\left(u \right)}}{7}$$$

The calculator will find the derivative of $$$\frac{\sqrt{7} \sin{\left(u \right)}}{7}$$$, with steps shown.

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Your Input

Find $$$\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right)$$$.

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 $$$c = \frac{\sqrt{7}}{7}$$$ and $$$f{\left(u \right)} = \sin{\left(u \right)}$$$:

$${\color{red}\left(\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right)\right)} = {\color{red}\left(\frac{\sqrt{7}}{7} \frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}$$

The derivative of the sine is $$$\frac{d}{du} \left(\sin{\left(u \right)}\right) = \cos{\left(u \right)}$$$:

$$\frac{\sqrt{7} {\color{red}\left(\frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}}{7} = \frac{\sqrt{7} {\color{red}\left(\cos{\left(u \right)}\right)}}{7}$$

Thus, $$$\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right) = \frac{\sqrt{7} \cos{\left(u \right)}}{7}$$$.

Answer

$$$\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right) = \frac{\sqrt{7} \cos{\left(u \right)}}{7}$$$A

Related Notes: Definition of Derivative , Derivatives of Elementary Functions , Table of Derivatives , Related Rates , Studying Derivative Graphically , Optimization Problems , Applications to Economics , Constant Multiple Rule , Sum and Difference Rules , Product Rule , Quotient Rule , Chain Rule , Derivative of Inverse Function