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Ufumbuzi - Tofauti

- \frac{\cos (x) \cot (x)}{\sin^{2} (x)} - \frac{\csc (x)}{\sin^{2} (x)}

- \frac{\cos{\left(x \right)} \cot{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{\csc{\left(x \right)}}{\sin^{2}{\left(x \right)}}

Tazama hatua

Maelezo kwa hatua

1. Suluhisha johofu

Kutumia sheria ya bidhaa ya vifungu.

$\frac{d}{d x} [\cot (x) \times \csc (x)] = \frac{d}{d x} [\cot (x)] \times \csc (x) + \cot (x) \times \frac{d}{d x} [\csc (x)]$

8 ziada steps

Kuipata mchanganyiko wa mabadiliko ya kazi ya kotanjenti.

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

Kotanjenti ya pembe ni sawa na cosine ya pembe iliyogawanywa na sine ya pembe.

$\frac{d}{d x} [\cot (x)] = \frac{d}{d x} [\frac{\cos (x)}{\sin (x)}]$

Kuhesabu kifungu cha kazi ya sehemu.

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

Kuipata mchanganyiko wa mabadiliko ya kazi ya kosaini.

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

Kuipata mchanganyiko wa mabadiliko ya kazi ya saini.

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

Kuzidisha idadi sawa pamoja.

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

Kuzidisha idadi sawa pamoja.

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

Kuunganisha istilahi hasi pamoja.

$\frac{- \sin {(x)}^{2} - \cos {(x)}^{2}}{\sin {(x)}^{2}} = \frac{- (\sin {(x)}^{2} + \cos {(x)}^{2})}{\sin {(x)}^{2}}$

Kipeo cha pili cha saini ya pembe sumuni na kipeo cha pili cha kosaini ya pambe hii hii ni sawa na moja wakati.

$\frac{- (\sin {(x)}^{2} + \cos {(x)}^{2})}{\sin {(x)}^{2}} = \frac{- 1}{\sin {(x)}^{2}}$

Kuweka alama ya nukta mbele ya kigawanya.

$\frac{- 1}{\sin {(x)}^{2}} = - \frac{1}{\sin {(x)}^{2}}$

2 ziada steps

Kuipata mchanganyiko wa mabadiliko ya kazi ya kosekanti.

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

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.

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

Kurahanisisha maneno ya hesabu.

$- \frac{1}{\sin^{2} (x)} \times \csc (x) + \cot (x) \times (- \frac{1}{\sin^{2} (x)} \times \cos (x)) = - \frac{\csc (x)}{\sin^{2} (x)} + \cot (x) \times (- \frac{1}{\sin^{2} (x)} \times \cos (x))$

Kurahanisisha maneno ya hesabu.

$- \frac{\csc (x)}{\sin^{2} (x)} + \cot (x) \times (- \frac{1}{\sin^{2} (x)} \times \cos (x)) = - \frac{\csc (x)}{\sin^{2} (x)} + \cot (x) \times (- \frac{\cos (x)}{\sin^{2} (x)})$

Kurahanisisha maneno ya hesabu.

$- \frac{\csc (x)}{\sin^{2} (x)} + \cot (x) \times (- \frac{\cos (x)}{\sin^{2} (x)}) = - \frac{\csc (x)}{\sin^{2} (x)} - \frac{\cos (x) \cot (x)}{\sin^{2} (x)}$

Kurahanisisha maneno ya hesabu.

$- \frac{\csc (x)}{\sin^{2} (x)} - \frac{\cos (x) \cot (x)}{\sin^{2} (x)} = - \frac{\cos (x) \cot (x)}{\sin^{2} (x)} - \frac{\csc (x)}{\sin^{2} (x)}$

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Ufumbuzi - Tofauti

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1. Suluhisha johofu

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