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