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Turunan kedua dari $$$- \sin{\left(x \right)}$$$

Kalkulator akan menghitung turunan kedua dari $$$- \sin{\left(x \right)}$$$, beserta langkah-langkahnya.

Kalkulator terkait: Kalkulator Turunan, Kalkulator Diferensiasi Logaritmik

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Masukan Anda

Temukan $$$\frac{d^{2}}{dx^{2}} \left(- \sin{\left(x \right)}\right)$$$.

Solusi

Tentukan turunan pertama $$$\frac{d}{dx} \left(- \sin{\left(x \right)}\right)$$$

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 $$$c = -1$$$ dan $$$f{\left(x \right)} = \sin{\left(x \right)}$$$:

$${\color{red}\left(\frac{d}{dx} \left(- \sin{\left(x \right)}\right)\right)} = {\color{red}\left(- \frac{d}{dx} \left(\sin{\left(x \right)}\right)\right)}$$

Turunan fungsi sinus adalah $$$\frac{d}{dx} \left(\sin{\left(x \right)}\right) = \cos{\left(x \right)}$$$:

$$- {\color{red}\left(\frac{d}{dx} \left(\sin{\left(x \right)}\right)\right)} = - {\color{red}\left(\cos{\left(x \right)}\right)}$$

Dengan demikian, $$$\frac{d}{dx} \left(- \sin{\left(x \right)}\right) = - \cos{\left(x \right)}$$$.

Selanjutnya, $$$\frac{d^{2}}{dx^{2}} \left(- \sin{\left(x \right)}\right) = \frac{d}{dx} \left(- \cos{\left(x \right)}\right)$$$

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 $$$c = -1$$$ dan $$$f{\left(x \right)} = \cos{\left(x \right)}$$$:

$${\color{red}\left(\frac{d}{dx} \left(- \cos{\left(x \right)}\right)\right)} = {\color{red}\left(- \frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)}$$

Turunan fungsi kosinus adalah $$$\frac{d}{dx} \left(\cos{\left(x \right)}\right) = - \sin{\left(x \right)}$$$:

$$- {\color{red}\left(\frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)} = - {\color{red}\left(- \sin{\left(x \right)}\right)}$$

Dengan demikian, $$$\frac{d}{dx} \left(- \cos{\left(x \right)}\right) = \sin{\left(x \right)}$$$.

Oleh karena itu, $$$\frac{d^{2}}{dx^{2}} \left(- \sin{\left(x \right)}\right) = \sin{\left(x \right)}$$$.

Jawaban

$$$\frac{d^{2}}{dx^{2}} \left(- \sin{\left(x \right)}\right) = \sin{\left(x \right)}$$$A


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