If y-tanx- then d2ydx2-

The correct option is D 2ydydx Given y=tan x ∴dydx=^2 x .......( 1) #160; #160; d^2ydx^2=2 x.( x .tan x )=2^2x tan x #160; ...

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Standard XII

Mathematics

Higher Order Derivatives

If y=tanx, ...

Question

If $y = tan x$ , then $\frac{d^{2} y}{d x^{2}} =$

x \frac{d y}{d x}

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2 x \frac{d y}{d x}

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2 y \frac{d y}{d x}

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y \frac{d y}{d x}

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Solution

The correct option is D $2 y \frac{d y}{d x}$
Given $y = tan x$
$∴ \frac{d y}{d x} = {sec}^{2} x . . . . . . . (1)$
$\frac{d^{2} y}{d x^{2}} = 2 sec x . (sec x . tan x) = 2 {sec}^{2} x tan x$ $. . . . . (2)$
substituting the value of ${sec}^{2} x$ from $(1)$ in $(2)$ we get,
$\Rightarrow \frac{d^{2} y}{d x^{2}} = 2 (\frac{d y}{d x}) tan x$
Also we have $y = tan x,$ substituting we get
$\Rightarrow \frac{d^{2} y}{d x^{2}} = 2 y \frac{d y}{d x}$
Hence, the answer is $2 y \frac{d y}{d x} .$

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If y=tanx, then d2ydx2=

The correct option is D 2ydydxGiven y=tanx∴dydx=sec2x.......(1) d2ydx2=2secx.(secx.tanx)=2sec2xtanx .....(2)substituting the value of sec2x from (1) in (2) we get,⇒d2ydx2=2(dydx)tanxAlso we have y=tanx, substituting we get ⇒d2ydx2=2ydydxHence, the answer is 2ydydx.

If $y = tan x$ , then $\frac{d^{2} y}{d x^{2}} =$