How can use the derivaties ddx(sin⁡x)=cos⁡x. ddx(tan⁡x)=sec2x,andddx(sec⁡x)=sec⁡xtan⁡x to remember the derivatives of cos⁡x,cot⁡x,andcsc⁡x?

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How can use the derivaties ddx(sin⁡x)=cos⁡x.  ddx(tan⁡x)=sec2x,andddx(sec⁡x)=sec⁡xtan⁡x to remember the derivatives of cos⁡x,cot⁡x,andcsc⁡x?

faldduE · Accepted Answer

Given,&amp;nbsp;d&amp;nbsp;dx&amp;nbsp;(sin⁡x)=cos⁡x,d&amp;nbsp;dx&amp;nbsp;(tan⁡x)=sec2x,&amp;nbsp;and&amp;nbsp;d&amp;nbsp;dx&amp;nbsp;(sec⁡x)=sec⁡xtan⁡x&amp;nbsp;Step 2&amp;nbsp;Now,&amp;nbsp;d&amp;nbsp;dx&amp;nbsp;(cos⁡x)=−sin⁡x,d&amp;nbsp;dx&amp;nbsp;(cot⁡x)=−csc2x,&amp;nbsp;and&amp;nbsp;d&amp;nbsp;dx&amp;nbsp;(csc⁡x)=−csc⁡xcot⁡x&amp;nbsp;To remember these derivatives, change cosx to sinx, secx to cscx, and tanx to cotx. Also keep in mind that the results of the above derivatives are negative.

How can use the derivaties d/(dx)(sin x)=cos x. d/(dx)(tan x)=sec^2x, and d/(dx)(sec x)=sec x tan x to remember the derivatives of cos x, cot x, and csc x?

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