|
|
|
|
|
|
|
|
|
|
|
|
Turunan dari $$$\frac{2 y}{x}$$$ terhadap $$$y$$$
Kalkulator terkait: Kalkulator Diferensiasi Logaritmik, Kalkulator Diferensiasi Implisit dengan Langkah-langkah
Masukan Anda
Temukan $$$\frac{d}{dy} \left(\frac{2 y}{x}\right)$$$.
Solusi
Terapkan aturan kelipatan konstanta $$$\frac{d}{dy} \left(c f{\left(y \right)}\right) = c \frac{d}{dy} \left(f{\left(y \right)}\right)$$$ dengan $$$c = \frac{2}{x}$$$ dan $$$f{\left(y \right)} = y$$$:
$${\color{red}\left(\frac{d}{dy} \left(\frac{2 y}{x}\right)\right)} = {\color{red}\left(\frac{2}{x} \frac{d}{dy} \left(y\right)\right)}$$Terapkan aturan pangkat $$$\frac{d}{dy} \left(y^{n}\right) = n y^{n - 1}$$$ dengan $$$n = 1$$$, dengan kata lain, $$$\frac{d}{dy} \left(y\right) = 1$$$:
$$\frac{2 {\color{red}\left(\frac{d}{dy} \left(y\right)\right)}}{x} = \frac{2 {\color{red}\left(1\right)}}{x}$$Dengan demikian, $$$\frac{d}{dy} \left(\frac{2 y}{x}\right) = \frac{2}{x}$$$.
Jawaban
$$$\frac{d}{dy} \left(\frac{2 y}{x}\right) = \frac{2}{x}$$$A