Derivative of sin(u)*|a| with respect to u

The calculator will find the derivative of $$$\sin{\left(u \right)} \left|{a}\right|$$$ with respect to $$$u$$$, with steps shown.

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Find $$$\frac{d}{du} \left(\sin{\left(u \right)} \left|{a}\right|\right)$$$.

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 $$$c = \left|{a}\right|$$$ and $$$f{\left(u \right)} = \sin{\left(u \right)}$$$:

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

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

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

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

Answer

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

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Derivative of $$$\sin{\left(u \right)} \left|{a}\right|$$$ with respect to $$$u$$$

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Solution

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