If y= tan x tan 2 x tan 3 x then (d y/d x) has the value equal to

Question

If y= tan x tan 2 x tan 3 x then (d y/d x) has the value equal to (A) 3 sec 2 3 x tan x tan 2 x+ sec 2 x tan 2 x tan 3 x+2 sec 2 2 x tan 3 x tan x (B) 2 y( operatornamecosec 2 x+2 operatornamecosec 4 x+3 operatornamecosec 6 x) (C) 3 sec 2 3 x-2 sec 2 2 x- sec 2 x (D)  sec 2 x+2 sec 2 2 x+3 sec 2 3 x

Tardigrade Admin · Accepted Answer

Correct answer is (a) 3 sec 2 3 x tan x tan 2 x+ sec 2 x tan 2 x tan 3 x+2 sec 2 2 x tan 3 x tan xCorrect answer is (b) 2 y( operatornamecosec 2 x+2 operatornamecosec 4 x+3 operatornamecosec 6 x)Correct answer is (c) 3 sec 2 3 x-2 sec 2 2 x- sec 2 x

Q. If $y = tan x tan 2 x tan 3 x$ then $\frac{d y}{d x}$ has the value equal to

$3 sec^{2} 3 x tan x tan 2 x + sec^{2} x tan 2 x tan 3 x + 2 sec^{2} 2 x tan 3 x tan x$

$2 y (cosec 2 x + 2 cosec 4 x + 3 cosec 6 x)$

$3 sec^{2} 3 x - 2 sec^{2} 2 x - sec^{2} x$

$sec^{2} x + 2 sec^{2} 2 x + 3 sec^{2} 3 x$

Correct answer is (a) $3 sec^{2} 3 x tan x tan 2 x + sec^{2} x tan 2 x tan 3 x + 2 sec^{2} 2 x tan 3 x tan x$ Correct answer is (b) $2 y (cosec 2 x + 2 cosec 4 x + 3 cosec 6 x)$ Correct answer is (c) $3 sec^{2} 3 x - 2 sec^{2} 2 x - sec^{2} x$

Q. If y=tanxtan2xtan3x then dxdy​ has the value equal to

3sec23xtanxtan2x+sec2xtan2xtan3x+2sec22xtan3xtanx

2y(cosec2x+2cosec4x+3cosec6x)

3sec23x−2sec22x−sec2x

sec2x+2sec22x+3sec23x