Find d - dx of y -tan xA- cos 2 xB- tan 2 xC- 2 xD- cosec2 x

D(tan⁡x )dx =d (sin⁡xcos⁡x )dx nbsp;=cos⁡ x d (sin⁡ x )dx sin⁡ x d(cos⁡ x)dxcos^2⁡x =cos⁡ x cos⁡ x sin⁡ x( sin ⁡x)cos^2⁡x =cos^2⁡x+sin^2⁡x cos^2⁡x =1cos^2⁡x ...

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Byju's Answer

Standard XI

Mathematics

Trigonometric Ratios of Compound Angles

Find d / dx o...

Question

Find $\frac{d}{d x}$ of $y = t a n x$ .

c o s^{2} x

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t a n^{2} x

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s e c^{2} x

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c o s e c^{2} x

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Solution

The correct option is C $s e c^{2} x$
$\frac{d (t a n x)}{d x} = \frac{d (\frac{s i n x}{c o s x})}{d x}$
$= \frac{c o s x \frac{d (s i n x)}{d x} - s i n x \frac{d (c o s x)}{d x}}{c o s^{2} x}$
$= \frac{c o s x c o s x - s i n x (- s i n x)}{c o s^{2} x}$
$= \frac{c o s^{2} x + s i n^{2} x}{c o s^{2} x} = \frac{1}{c o s^{2} x} = s e c^{2} x$

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Find ddx of y=tan x.

The correct option is C sec2 xd(tanx)dx=d(sinxcosx)dx =cos xd(sin x)dx−sin xd(cos x)dxcos2x =cos x cos x−sin x(−sin x)cos2x =cos2x+sin2xcos2x=1cos2x=sec2x

Find $\frac{d}{d x}$ of $y = t a n x$ .