|
|
|
|
|
|
|
|
|
|
|
|
Turunan dari $$$\cot^{2}{\left(x \right)}$$$
Kalkulator terkait: Kalkulator Diferensiasi Logaritmik, Kalkulator Diferensiasi Implisit dengan Langkah-langkah
Masukan Anda
Temukan $$$\frac{d}{dx} \left(\cot^{2}{\left(x \right)}\right)$$$.
Solusi
Fungsi $$$\cot^{2}{\left(x \right)}$$$ merupakan komposisi $$$f{\left(g{\left(x \right)} \right)}$$$ dari dua fungsi $$$f{\left(u \right)} = u^{2}$$$ dan $$$g{\left(x \right)} = \cot{\left(x \right)}$$$.
Terapkan aturan rantai $$$\frac{d}{dx} \left(f{\left(g{\left(x \right)} \right)}\right) = \frac{d}{du} \left(f{\left(u \right)}\right) \frac{d}{dx} \left(g{\left(x \right)}\right)$$$:
$${\color{red}\left(\frac{d}{dx} \left(\cot^{2}{\left(x \right)}\right)\right)} = {\color{red}\left(\frac{d}{du} \left(u^{2}\right) \frac{d}{dx} \left(\cot{\left(x \right)}\right)\right)}$$Terapkan aturan pangkat $$$\frac{d}{du} \left(u^{n}\right) = n u^{n - 1}$$$ dengan $$$n = 2$$$:
$${\color{red}\left(\frac{d}{du} \left(u^{2}\right)\right)} \frac{d}{dx} \left(\cot{\left(x \right)}\right) = {\color{red}\left(2 u\right)} \frac{d}{dx} \left(\cot{\left(x \right)}\right)$$Kembalikan ke variabel semula:
$$2 {\color{red}\left(u\right)} \frac{d}{dx} \left(\cot{\left(x \right)}\right) = 2 {\color{red}\left(\cot{\left(x \right)}\right)} \frac{d}{dx} \left(\cot{\left(x \right)}\right)$$Turunan dari kotangen adalah $$$\frac{d}{dx} \left(\cot{\left(x \right)}\right) = - \csc^{2}{\left(x \right)}$$$:
$$2 \cot{\left(x \right)} {\color{red}\left(\frac{d}{dx} \left(\cot{\left(x \right)}\right)\right)} = 2 \cot{\left(x \right)} {\color{red}\left(- \csc^{2}{\left(x \right)}\right)}$$Dengan demikian, $$$\frac{d}{dx} \left(\cot^{2}{\left(x \right)}\right) = - 2 \cot{\left(x \right)} \csc^{2}{\left(x \right)}$$$.
Jawaban
$$$\frac{d}{dx} \left(\cot^{2}{\left(x \right)}\right) = - 2 \cot{\left(x \right)} \csc^{2}{\left(x \right)}$$$A