If y = tan : x then (d2 y/dx2) =

Question

If y = tan : x then (d2 y/dx2) = (A)  1 + y2 (B) 2y ( 1 + y2) (C) y( 1 + y2) (D) 2y(1 -y2)

Tardigrade Admin · Accepted Answer

Given, y = tan : x Differentiating w.r.t. 'x' on both sides (dy/dx) = sec2 x Taking again derivative w.r.t. 'x' : : :(d2 y/dx2) =2 sec x . sec x tan x = 2sec2 x tan x = 2 tan x (1 + tan2 x) = 2y (1 + y2)

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

$1 + y^{2}$

$2 y (1 + y^{2})$

$y (1 + y^{2})$

$2 y (1 - y^{2})$

Given, $y = tan x$
Differentiating w.r.t. $^{'} x^{'}$ on both sides $\frac{d y}{d x} = se c^{2} x$
Taking again derivative w.r.t. $^{'} x^{'} \frac{d ^{2} y}{d x ^{2}} = 2 sec x . sec x tan x$
$= 2 se c^{2} x tan x = 2 tan x (1 + t a n^{2} x)$
$= 2 y (1 + y^{2})$

Q. If y=tanx then dx2d2y​ =

1+y2

2y(1+y2)

y(1+y2)

2y(1−y2)