Turunan dari $$$\pi \left(z - 1\right)$$$ terhadap $$$\pi$$$
Kalkulator terkait: Kalkulator Diferensiasi Logaritmik, Kalkulator Diferensiasi Implisit dengan Langkah-langkah
Masukan Anda
Temukan $$$\frac{d}{d\pi} \left(\pi \left(z - 1\right)\right)$$$.
Solusi
Terapkan aturan kelipatan konstanta $$$\frac{d}{d\pi} \left(c f{\left(\pi \right)}\right) = c \frac{d}{d\pi} \left(f{\left(\pi \right)}\right)$$$ dengan $$$c = z - 1$$$ dan $$$f{\left(\pi \right)} = \pi$$$:
$${\color{red}\left(\frac{d}{d\pi} \left(\pi \left(z - 1\right)\right)\right)} = {\color{red}\left(\left(z - 1\right) \frac{d}{d\pi} \left(\pi\right)\right)}$$Terapkan aturan pangkat $$$\frac{d}{d\pi} \left(\pi^{n}\right) = n \pi^{n - 1}$$$ dengan $$$n = 1$$$, dengan kata lain, $$$\frac{d}{d\pi} \left(\pi\right) = 1$$$:
$$\left(z - 1\right) {\color{red}\left(\frac{d}{d\pi} \left(\pi\right)\right)} = \left(z - 1\right) {\color{red}\left(1\right)}$$Dengan demikian, $$$\frac{d}{d\pi} \left(\pi \left(z - 1\right)\right) = z - 1$$$.
Jawaban
$$$\frac{d}{d\pi} \left(\pi \left(z - 1\right)\right) = z - 1$$$A