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