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Turunan kedua dari $$$x^{2}$$$
Kalkulator terkait: Kalkulator Turunan, Kalkulator Diferensiasi Logaritmik
Masukan Anda
Temukan $$$\frac{d^{2}}{dx^{2}} \left(x^{2}\right)$$$.
Solusi
Tentukan turunan pertama $$$\frac{d}{dx} \left(x^{2}\right)$$$
Terapkan aturan pangkat $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ dengan $$$n = 2$$$:
$${\color{red}\left(\frac{d}{dx} \left(x^{2}\right)\right)} = {\color{red}\left(2 x\right)}$$Dengan demikian, $$$\frac{d}{dx} \left(x^{2}\right) = 2 x$$$.
Selanjutnya, $$$\frac{d^{2}}{dx^{2}} \left(x^{2}\right) = \frac{d}{dx} \left(2 x\right)$$$
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 $$$c = 2$$$ dan $$$f{\left(x \right)} = x$$$:
$${\color{red}\left(\frac{d}{dx} \left(2 x\right)\right)} = {\color{red}\left(2 \frac{d}{dx} \left(x\right)\right)}$$Terapkan aturan pangkat $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ dengan $$$n = 1$$$, dengan kata lain, $$$\frac{d}{dx} \left(x\right) = 1$$$:
$$2 {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = 2 {\color{red}\left(1\right)}$$Dengan demikian, $$$\frac{d}{dx} \left(2 x\right) = 2$$$.
Oleh karena itu, $$$\frac{d^{2}}{dx^{2}} \left(x^{2}\right) = 2$$$.
Jawaban
$$$\frac{d^{2}}{dx^{2}} \left(x^{2}\right) = 2$$$A