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Turunan kedua dari $$$\sinh{\left(x \right)}$$$
Kalkulator terkait: Kalkulator Turunan, Kalkulator Diferensiasi Logaritmik
Masukan Anda
Temukan $$$\frac{d^{2}}{dx^{2}} \left(\sinh{\left(x \right)}\right)$$$.
Solusi
Tentukan turunan pertama $$$\frac{d}{dx} \left(\sinh{\left(x \right)}\right)$$$
Turunan dari sinus hiperbolik adalah $$$\frac{d}{dx} \left(\sinh{\left(x \right)}\right) = \cosh{\left(x \right)}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\sinh{\left(x \right)}\right)\right)} = {\color{red}\left(\cosh{\left(x \right)}\right)}$$Dengan demikian, $$$\frac{d}{dx} \left(\sinh{\left(x \right)}\right) = \cosh{\left(x \right)}$$$.
Selanjutnya, $$$\frac{d^{2}}{dx^{2}} \left(\sinh{\left(x \right)}\right) = \frac{d}{dx} \left(\cosh{\left(x \right)}\right)$$$
Turunan dari kosinus hiperbolik adalah $$$\frac{d}{dx} \left(\cosh{\left(x \right)}\right) = \sinh{\left(x \right)}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\cosh{\left(x \right)}\right)\right)} = {\color{red}\left(\sinh{\left(x \right)}\right)}$$Dengan demikian, $$$\frac{d}{dx} \left(\cosh{\left(x \right)}\right) = \sinh{\left(x \right)}$$$.
Oleh karena itu, $$$\frac{d^{2}}{dx^{2}} \left(\sinh{\left(x \right)}\right) = \sinh{\left(x \right)}$$$.
Jawaban
$$$\frac{d^{2}}{dx^{2}} \left(\sinh{\left(x \right)}\right) = \sinh{\left(x \right)}$$$A