Find the derivative of `f(tanx)wdotrdottg(secx)a tx=pi/4,` where `f^(prime)(1)=2a n dg^(prime)(sqrt(2))=4.`

Explanation

`"Let "u=f(tan x) and v=g(sec x).` Therefore,
`(du)/(dv)=f'(tan x) sec^(2)x`
`" and "(dv)/(dx)=g'(sec x) sec x tan x`
`therefore" "(du)/(dv)=(du)/(dx)//(dv)/(dx)=(f'(tan x) sec^(2)x)/(g'(sec x) sec x tan x)`
`"or "[(du)/(dv)]_(x=(pi)/(4))=(f'(tan""(pi)/(4)))/(g'(sec""(pi)/(4))sin""(pi)/(4))=(f'(1)sqrt(2))/(g'(sqrt(2)))`
`=(2sqrt(2))/(4)=(1)/(sqrt(2))`