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Turunan dari $$$\frac{2 \sin{\left(u \right)}}{\left|{y}\right|}$$$ terhadap $$$u$$$
Kalkulator terkait: Kalkulator Diferensiasi Logaritmik, Kalkulator Diferensiasi Implisit dengan Langkah-langkah
Masukan Anda
Temukan $$$\frac{d}{du} \left(\frac{2 \sin{\left(u \right)}}{\left|{y}\right|}\right)$$$.
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 $$$c = \frac{2}{\left|{y}\right|}$$$ dan $$$f{\left(u \right)} = \sin{\left(u \right)}$$$:
$${\color{red}\left(\frac{d}{du} \left(\frac{2 \sin{\left(u \right)}}{\left|{y}\right|}\right)\right)} = {\color{red}\left(\frac{2}{\left|{y}\right|} \frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}$$Turunan fungsi sinus adalah $$$\frac{d}{du} \left(\sin{\left(u \right)}\right) = \cos{\left(u \right)}$$$:
$$\frac{2 {\color{red}\left(\frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}}{\left|{y}\right|} = \frac{2 {\color{red}\left(\cos{\left(u \right)}\right)}}{\left|{y}\right|}$$Dengan demikian, $$$\frac{d}{du} \left(\frac{2 \sin{\left(u \right)}}{\left|{y}\right|}\right) = \frac{2 \cos{\left(u \right)}}{\left|{y}\right|}$$$.
Jawaban
$$$\frac{d}{du} \left(\frac{2 \sin{\left(u \right)}}{\left|{y}\right|}\right) = \frac{2 \cos{\left(u \right)}}{\left|{y}\right|}$$$A