Turunan dari $$$- \frac{\pi}{6} + z$$$ terhadap $$$\pi$$$
Kalkulator terkait: Kalkulator Diferensiasi Logaritmik, Kalkulator Diferensiasi Implisit dengan Langkah-langkah
Masukan Anda
Temukan $$$\frac{d}{d\pi} \left(- \frac{\pi}{6} + z\right)$$$.
Solusi
Turunan dari jumlah/selisih adalah jumlah/selisih dari turunan:
$${\color{red}\left(\frac{d}{d\pi} \left(- \frac{\pi}{6} + z\right)\right)} = {\color{red}\left(- \frac{d}{d\pi} \left(\frac{\pi}{6}\right) + \frac{dz}{d\pi}\right)}$$Turunan dari suatu konstanta adalah $$$0$$$:
$${\color{red}\left(\frac{dz}{d\pi}\right)} - \frac{d}{d\pi} \left(\frac{\pi}{6}\right) = {\color{red}\left(0\right)} - \frac{d}{d\pi} \left(\frac{\pi}{6}\right)$$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 $$$c = \frac{1}{6}$$$ dan $$$f{\left(\pi \right)} = \pi$$$:
$$- {\color{red}\left(\frac{d}{d\pi} \left(\frac{\pi}{6}\right)\right)} = - {\color{red}\left(\frac{\frac{d}{d\pi} \left(\pi\right)}{6}\right)}$$Terapkan aturan pangkat $$$\frac{d}{d\pi} \left(\pi^{n}\right) = n \pi^{n - 1}$$$ dengan $$$n = 1$$$, dengan kata lain, $$$\frac{d}{d\pi} \left(\pi\right) = 1$$$:
$$- \frac{{\color{red}\left(\frac{d}{d\pi} \left(\pi\right)\right)}}{6} = - \frac{{\color{red}\left(1\right)}}{6}$$Dengan demikian, $$$\frac{d}{d\pi} \left(- \frac{\pi}{6} + z\right) = - \frac{1}{6}$$$.
Jawaban
$$$\frac{d}{d\pi} \left(- \frac{\pi}{6} + z\right) = - \frac{1}{6}$$$A