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Turunan dari $$$\frac{\sin{\left(u \right)}}{5}$$$

Kalkulator akan menentukan turunan dari $$$\frac{\sin{\left(u \right)}}{5}$$$, dengan langkah-langkah yang ditampilkan.

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Masukan Anda

Temukan $$$\frac{d}{du} \left(\frac{\sin{\left(u \right)}}{5}\right)$$$.

Solusi

Terapkan aturan kelipatan konstanta $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$ dengan $$$c = \frac{1}{5}$$$ dan $$$f{\left(u \right)} = \sin{\left(u \right)}$$$:

$${\color{red}\left(\frac{d}{du} \left(\frac{\sin{\left(u \right)}}{5}\right)\right)} = {\color{red}\left(\frac{\frac{d}{du} \left(\sin{\left(u \right)}\right)}{5}\right)}$$

Turunan fungsi sinus adalah $$$\frac{d}{du} \left(\sin{\left(u \right)}\right) = \cos{\left(u \right)}$$$:

$$\frac{{\color{red}\left(\frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}}{5} = \frac{{\color{red}\left(\cos{\left(u \right)}\right)}}{5}$$

Dengan demikian, $$$\frac{d}{du} \left(\frac{\sin{\left(u \right)}}{5}\right) = \frac{\cos{\left(u \right)}}{5}$$$.

Jawaban

$$$\frac{d}{du} \left(\frac{\sin{\left(u \right)}}{5}\right) = \frac{\cos{\left(u \right)}}{5}$$$A

Catatan Terkait: 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