Question

if y = (1+2 tan x ) (5+4 cos x ) find dy/dx​

Answer 1

Answer:

f y = (1+2 tan x ) (5+4 cos x ) find dy/dx

Answer 2

$\large\red{\sf\underline{\underline{Question}}}:$

• If y = (1+ 2tan x ) (5+ 4cos x ) , Find dy/dx .

$\large\red{\sf\underline{\underline{Solution}}}:$

By product rule , we know that :

• (UV)' = U'V + V'U

$\sf\dfrac{dy}{dx} = \dfrac{d}{dx}[(1+ 2\tan x )].(5+ 4\cos x ) + \dfrac{d}{dx}[(5+ 4\cos x )](1+ 2\tan x )$

$\sf\dfrac{dy}{dx} = 2\sec^2 x (5 +4\cos x ) + 4(-\sin x) . (1+ 2\tan x )$

$\sf\dfrac{dy}{dx} = 10\sec^2 x + 8\sec^2 x.\cos x -4\sin x -8\sin x.\tan x$

$\sf\dfrac{dy}{dx} = 10\sec^2 x + 8\sec x -4\sin x -8\sin x.\tan x$

$\large\red{\sf\underline{\underline{Therefore}}},$

• dy/dx of y = (1+2 tan x ) (5+4 cos x ) is 10sec²x + 8sec x -4sin x -8sin x.tan x

Formulas to know :

• (sin x)' = cos x
• (cos x)' = -sin x
• (tan x) ' = sec² x
• (cot x)' = - cosec² x
• (cosec x)' = -cosec x. cot x
• $\sf (x^{n} )' = n.x^{n-1}$