यदि `y=(1+2tan x)(5+4cos x)` तो गुणनफल नियम से `(dy)/(dx)` का मान ज्ञात कीजिएः

Explanation

`y=(1+2tan x)(5+4cos x)`
`Rightarrow (dy)/(dx)=(1+2tan x)(d)/(dx)(5+4cos x)+(5+4 cos x)(d)/(dx)(1+2tanx)`
`=(1+2tan x)(-4 sin x)+(5+4 cos x)(2 sec^(2)x)`
`=-4sin x+8 tan x sin x+10sec^(2)x+8sec x`
`=-4sin x+10 tan x sin x+10sec^(2)x+8sec x`
`=-4sin x+10 sec^(2)x +8cosx`