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Turunan dari $$$2 \sinh{\left(v \right)}$$$
Kalkulator terkait: Kalkulator Diferensiasi Logaritmik, Kalkulator Diferensiasi Implisit dengan Langkah-langkah
Masukan Anda
Temukan $$$\frac{d}{dv} \left(2 \sinh{\left(v \right)}\right)$$$.
Solusi
Terapkan aturan kelipatan konstanta $$$\frac{d}{dv} \left(c f{\left(v \right)}\right) = c \frac{d}{dv} \left(f{\left(v \right)}\right)$$$ dengan $$$c = 2$$$ dan $$$f{\left(v \right)} = \sinh{\left(v \right)}$$$:
$${\color{red}\left(\frac{d}{dv} \left(2 \sinh{\left(v \right)}\right)\right)} = {\color{red}\left(2 \frac{d}{dv} \left(\sinh{\left(v \right)}\right)\right)}$$Turunan dari sinus hiperbolik adalah $$$\frac{d}{dv} \left(\sinh{\left(v \right)}\right) = \cosh{\left(v \right)}$$$:
$$2 {\color{red}\left(\frac{d}{dv} \left(\sinh{\left(v \right)}\right)\right)} = 2 {\color{red}\left(\cosh{\left(v \right)}\right)}$$Dengan demikian, $$$\frac{d}{dv} \left(2 \sinh{\left(v \right)}\right) = 2 \cosh{\left(v \right)}$$$.
Jawaban
$$$\frac{d}{dv} \left(2 \sinh{\left(v \right)}\right) = 2 \cosh{\left(v \right)}$$$A