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Ufumbuzi - Tofauti

- \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)}}

Tazama hatua

Maelezo kwa hatua

1. Suluhisha johofu

6 ziada steps

Kuhesabu kifungu cha kazi ya kotangent kutumia sheria ya mfuatano.

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

Kufunua kazi kwa sheria ya mfuatano.

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

Kuhesabu kifungu cha kazi ya kotangent kutumia sheria ya mfuatano.

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

Kosikanti ya pembe ni sawa na moja iliyogawanywa na sine ya pembe.

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

Kuhesabu kifungu cha kazi ya kubaliana.

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

Kuipata mchanganyiko wa mabadiliko ya kazi ya saini.

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

Uzidishaji unaweza kikundi tofauti, lakini matokeo yanabaki yale yale.

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

Kurudisha kigezo katika kazi.

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

Kutumia sheria ya bidhaa ya vifungu.

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

Mchanganyiko wa mabadiliko ya thamani ya kudumu ni sawa na sifuri.

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

Kuzidisha idadi kwa sifuri daima hutoa sifuri.

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

Kuongeza sifuri kwa idadi, ambayo haibadilishi thamani yake.

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

Kuhesabu kifungu cha x iliyoinuka kwa nguvu ya n.

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

Kupunguza moja kutoka kwenye namba.

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

Uzidishaji unaweza kikundi tofauti, lakini matokeo yanabaki yale yale.

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

Kuzidisha vigezo mbili pamoja.

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

Kurahanisisha maneno ya hesabu.

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

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Ufumbuzi - Tofauti

Maelezo kwa hatua

1. Suluhisha johofu

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