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Solusi - Derivatif

- \frac{15 x^{2} \cos (x)}{\sin^{2} (5 x^{3})}

- \frac{15 x^{2} \cos{\left(x \right)}}{\sin^{2}{\left(5 x^{3} \right)}}

Lihat langkah

Penjelasan langkah demi langkah

1. Selesaikan turunan

6 tambahan langkah

Menghitung turunan dari fungsi cosecan menggunakan aturan rantai.

$\frac{d}{d x} [\csc (5 x^{3})] = - \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times \frac{d}{d x} [5 x^{3}]$

Mendekomposisi fungsi untuk aturan rantai.

$\frac{d}{d x} [\csc (5 x^{3})] = \frac{d}{d x} [\csc (x)] \times \frac{d}{d x} [5 x^{3}]$

Menghitung turunan dari fungsi cosecan menggunakan aturan rantai.

$\frac{d}{d x} [\csc (5 x^{3})] = - \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times \frac{d}{d x} [5 x^{3}]$

Cosecan dari sebuah sudut sama dengan satu dibagi dengan sinus sudut tersebut.

$\frac{d}{d x} [\csc (x)] = \frac{d}{d x} [\frac{1}{\sin (x)}]$

Menghitung turunan dari sebuah rekiprokal.

$\frac{d}{d x} [\frac{1}{\sin (x)}] = - \frac{1}{\sin {(x)}^{2}} \times \frac{d}{d x} [\sin (x)]$

Menghitung turunan dari fungsi sinus.

$- \frac{1}{\sin {(x)}^{2}} \times \frac{d}{d x} [\sin (x)] = - \frac{1}{\sin {(x)}^{2}} \times \cos (x)$

Perkalian dapat dikelompokkan secara berbeda, tetapi hasilnya tetap sama.

$(- \frac{1}{\sin {(x)}^{2}} \times \cos (x)) \times \frac{d}{d x} [5 x^{3}] = - \frac{1}{\sin {(x)}^{2}} \times \cos (x) \times \frac{d}{d x} [5 x^{3}]$

Menggantikan variabel kembali ke dalam fungsi.

$- \frac{1}{\sin {(x)}^{2}} \times \cos (x) \times \frac{d}{d x} [5 x^{3}] = - \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times \frac{d}{d x} [5 x^{3}]$

Menerapkan aturan perkalian turunan.

$- \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times \frac{d}{d x} [5 x^{3}] = - \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (\frac{d}{d x} [5] \times x^{3} + 5 \times \frac{d}{d x} [x^{3}])$

Turunan dari sebuah nilai konstan selalu nol.

$- \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (\frac{d}{d x} [5] \times x^{3} + 5 \times \frac{d}{d x} [x^{3}]) = - \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (0 x^{3} + 5 \times \frac{d}{d x} [x^{3}])$

Mengalikan sebuah angka dengan nol selalu menghasilkan nol.

$- \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (0 x^{3} + 5 \times \frac{d}{d x} [x^{3}]) = - \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (0 + 5 \times \frac{d}{d x} [x^{3}])$

Menambahkan nol ke sebuah angka, yang tidak mengubah nilai angka tersebut.

$- \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (0 + 5 \times \frac{d}{d x} [x^{3}]) = - \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (5 \times \frac{d}{d x} [x^{3}])$

Menghitung turunan dari x dipangkatkan dengan n.

$- \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (5 \times \frac{d}{d x} [x^{3}]) = - \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (5 \times (3 x^{3 - 1}))$

Mengurangkan satu dari sebuah angka.

$- \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (5 \times (3 x^{3 - 1})) = - \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (5 \times (3 x^{2}))$

Perkalian dapat dikelompokkan secara berbeda, tetapi hasilnya tetap sama.

$- \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (5 \times (3 x^{2})) = - \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times ((5 \times 3) \times x^{2})$

Mengalikan dua bilangan bulat bersama-sama.

$- \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times ((5 \times 3) \times x^{2}) = - \frac{1}{\sin {(5 x^{3})}^{2}} \times \cos (x) \times (15 x^{2})$

Menyederhanakan ekspresi aritmatika.

$- \frac{1}{\sin^{2} (5 x^{3})} \times \cos (x) \times (15 x^{2}) = - \frac{15 x^{2} \cos (x)}{\sin^{2} (5 x^{3})}$

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Istilah dan topik

Derivative

Solusi - Derivatif

Penjelasan langkah demi langkah

1. Selesaikan turunan

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