# 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?

How can use the derivaties $\frac{d}{dx}\left(\mathrm{sin}x\right)=\mathrm{cos}x$.
$\frac{d}{dx}\left(\mathrm{tan}x\right)={\mathrm{sec}}^{2}x,\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\frac{d}{dx}\left(\mathrm{sec}x\right)=\mathrm{sec}x\mathrm{tan}x$ to remember the derivatives of $\mathrm{cos}x,\mathrm{cot}x,\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathrm{csc}x$?
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faldduE
Given,
$\frac{d}{dx}\left(\mathrm{sin}x\right)=\mathrm{cos}x,\frac{d}{dx}\left(\mathrm{tan}x\right)={\mathrm{sec}}^{2}x,\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\frac{d}{dx}\left(\mathrm{sec}x\right)=\mathrm{sec}x\mathrm{tan}x$
Step 2
Now,
$\frac{d}{dx}\left(\mathrm{cos}x\right)=-\mathrm{sin}x,\frac{d}{dx}\left(\mathrm{cot}x\right)=-{\mathrm{csc}}^{2}x,\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\frac{d}{dx}\left(\mathrm{csc}x\right)=-\mathrm{csc}x\mathrm{cot}x$
Therefore to remember these derivatives, replace cosx by sinx, secx by cscx and tanx by cotx and also note that the above derivative results are negative.