यदि `y=(x tan x)/(sec x +tan x)` तो `(dy)/(dx)` का मान ज्ञात कीजिएः

Explanation

दिया है `y=(x tan x)/(sec x+tan x)`
भागफल विधि से
`(dy)/(dx)=((sec x+tan x)(d)/(dx)(x tan x)-x tan x(d)/(dx)(sec x+tan x))/((sec x+tan x)^(2))`
`=((sec x+tan x)[x,(d)/(dx)(tan x)+tan x.(d)/(dx)(x)]-xtan x[(d)/(dx)(sec x)+(d)/(dx)(tan x)])/((sec x+tan x)^(2))`
`=((sec x+tan x)(x sec ^(2)x +tan x)-xtan x(sec x tan x+sec^(2)x))/((sec x+tan x)^(2))`
`=(x sec^3x +x tan sec^(2)x+sec x tan x+tan^(2)x-x sec x tan^(2)x-xtan x sec^(2)x)/((sec x+tan x)^(2))`
`=(x secx(sec^(2)x-tan^(2)x)+tan x(sec x+tan x))/((sec x+tan x)^(2))`
`=(x secx(secx-tanx)+tan x)/(sec x+tan x)`