यदि `y=tan x + sec x`, तो सिद्ध कीजिये कि `(d^(2)y)/(dx^(2))=("cos x")/((1-sin c)^(2))`.

Explanation

`y=tanx+secx`
या `(dy)/(dx)=sec^(2)x+sec x tanx`
या `(dy)/(dx)=secx(sec x+ tan x)`
या `(d^(2)y)/(dx^(2))=sec x tan x (sec x + tan x)+sec x (sec x tan x + sec^(2)x)`
`=sec x tan x (sec x + tan x ) + sec^(2)x (tan x + sec x)`
`=(sec x + tan x) (sec x tan x +sec^(2) x)`
`=(sec x + tan x) sec x (tan x + sec x)`
`=sec x (sec x + tan x ) ^(2)`
`=(1)/(cos x) ((1)/(cos x) + (sin x)/(cos x))^(2)`
`=(1+sin x)^(2)/(cosx cos ^(2)x)`
`=((1+sinx)^(2))/(cos^(3)x)=((1+sin x)^(2)cos x)/(cos^(4)x)`
`=((1+sinx)^(2)cos x)/((1+sinx)^(2)(1-sinx)^(2))`
`=(cos x)/((1-sin x)^(2))` ( इति सिध्दम )