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