Turunan dari $$$\frac{5^{\frac{3}{4}} x}{5}$$$
Kalkulator terkait: Kalkulator Diferensiasi Logaritmik, Kalkulator Diferensiasi Implisit dengan Langkah-langkah
Masukan Anda
Temukan $$$\frac{d}{dx} \left(\frac{5^{\frac{3}{4}} x}{5}\right)$$$.
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 $$$c = \frac{5^{\frac{3}{4}}}{5}$$$ dan $$$f{\left(x \right)} = x$$$:
$${\color{red}\left(\frac{d}{dx} \left(\frac{5^{\frac{3}{4}} x}{5}\right)\right)} = {\color{red}\left(\frac{5^{\frac{3}{4}}}{5} \frac{d}{dx} \left(x\right)\right)}$$Terapkan aturan pangkat $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ dengan $$$n = 1$$$, dengan kata lain, $$$\frac{d}{dx} \left(x\right) = 1$$$:
$$\frac{5^{\frac{3}{4}} {\color{red}\left(\frac{d}{dx} \left(x\right)\right)}}{5} = \frac{5^{\frac{3}{4}} {\color{red}\left(1\right)}}{5}$$Dengan demikian, $$$\frac{d}{dx} \left(\frac{5^{\frac{3}{4}} x}{5}\right) = \frac{5^{\frac{3}{4}}}{5}$$$.
Jawaban
$$$\frac{d}{dx} \left(\frac{5^{\frac{3}{4}} x}{5}\right) = \frac{5^{\frac{3}{4}}}{5}$$$A