Turunan dari $$$\frac{5 \cosh{\left(u \right)}}{2}$$$
Kalkulator terkait: Kalkulator Diferensiasi Logaritmik, Kalkulator Diferensiasi Implisit dengan Langkah-langkah
Masukan Anda
Temukan $$$\frac{d}{du} \left(\frac{5 \cosh{\left(u \right)}}{2}\right)$$$.
Solusi
Terapkan aturan kelipatan konstanta $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$ dengan $$$c = \frac{5}{2}$$$ dan $$$f{\left(u \right)} = \cosh{\left(u \right)}$$$:
$${\color{red}\left(\frac{d}{du} \left(\frac{5 \cosh{\left(u \right)}}{2}\right)\right)} = {\color{red}\left(\frac{5 \frac{d}{du} \left(\cosh{\left(u \right)}\right)}{2}\right)}$$Turunan dari kosinus hiperbolik adalah $$$\frac{d}{du} \left(\cosh{\left(u \right)}\right) = \sinh{\left(u \right)}$$$:
$$\frac{5 {\color{red}\left(\frac{d}{du} \left(\cosh{\left(u \right)}\right)\right)}}{2} = \frac{5 {\color{red}\left(\sinh{\left(u \right)}\right)}}{2}$$Dengan demikian, $$$\frac{d}{du} \left(\frac{5 \cosh{\left(u \right)}}{2}\right) = \frac{5 \sinh{\left(u \right)}}{2}$$$.
Jawaban
$$$\frac{d}{du} \left(\frac{5 \cosh{\left(u \right)}}{2}\right) = \frac{5 \sinh{\left(u \right)}}{2}$$$A