Question

find the festive of tan x by using u/v rule​

Answer 1

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Answer 2

Question:- Find  the derivative of tanx by using u/v rule

Answer: sec²x

Step-by-step explanation:

We know  that,

tanx = sinx/cosx

$\frac{d(\sin x)}{dx}=\cos x$

and,

$\frac{d(\cos x)}{dx}=-\sin x$

And u/v rule:-

$\frac{d(u/v)}{dx}=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}$

Now,

$\frac{d\tan x}{dx}=\frac{d\sin x/\cos x}{dx}\\\;\\=\frac{\cos x.\frac{d\sin x}{dx}-\sin x.\frac{d\cos x}{dx}}{\cos^2x}\\\;\\=\frac{\cos x.\cos x-\sin x(-\sin x)}{\cos^2x}\\\;\\=\frac{\cos^2x+\sin^2x}{\cos^2x}\\\;\\=\frac{1}{\cos^2x}\;\;\;\;\;\;\;\;( \because\sin^2x+\cos^x=1)\\\;\\=\sec^2x\;\;\;\;\;\;\;\;(\because\sec x=\frac{1}{\cos x})$