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