Turunan dari $$$- x \sin{\left(\frac{1}{2} \right)} + 1$$$
Kalkulator terkait: Kalkulator Diferensiasi Logaritmik, Kalkulator Diferensiasi Implisit dengan Langkah-langkah
Masukan Anda
Temukan $$$\frac{d}{dx} \left(- x \sin{\left(\frac{1}{2} \right)} + 1\right)$$$.
Solusi
Turunan dari jumlah/selisih adalah jumlah/selisih dari turunan:
$${\color{red}\left(\frac{d}{dx} \left(- x \sin{\left(\frac{1}{2} \right)} + 1\right)\right)} = {\color{red}\left(- \frac{d}{dx} \left(x \sin{\left(\frac{1}{2} \right)}\right) + \frac{d}{dx} \left(1\right)\right)}$$Turunan dari suatu konstanta adalah $$$0$$$:
$${\color{red}\left(\frac{d}{dx} \left(1\right)\right)} - \frac{d}{dx} \left(x \sin{\left(\frac{1}{2} \right)}\right) = {\color{red}\left(0\right)} - \frac{d}{dx} \left(x \sin{\left(\frac{1}{2} \right)}\right)$$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 $$$c = \sin{\left(\frac{1}{2} \right)}$$$ dan $$$f{\left(x \right)} = x$$$:
$$- {\color{red}\left(\frac{d}{dx} \left(x \sin{\left(\frac{1}{2} \right)}\right)\right)} = - {\color{red}\left(\sin{\left(\frac{1}{2} \right)} \frac{d}{dx} \left(x\right)\right)}$$Terapkan aturan pangkat $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ dengan $$$n = 1$$$, dengan kata lain, $$$\frac{d}{dx} \left(x\right) = 1$$$:
$$- \sin{\left(\frac{1}{2} \right)} {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = - \sin{\left(\frac{1}{2} \right)} {\color{red}\left(1\right)}$$Dengan demikian, $$$\frac{d}{dx} \left(- x \sin{\left(\frac{1}{2} \right)} + 1\right) = - \sin{\left(\frac{1}{2} \right)}$$$.
Jawaban
$$$\frac{d}{dx} \left(- x \sin{\left(\frac{1}{2} \right)} + 1\right) = - \sin{\left(\frac{1}{2} \right)}$$$A