`Differential `e^(tanx)`with respect to sin x.

Explanation

`Let y_(1)=e^(tanx) " and " y_(2)=sin x `
`therefore dy_(1)/dx=d/dx e tan x`
`=e^tan x.d/dxe^tan x`
`e^tan x.s ec^2 x `
and `dy_(1)/dy_(2)=(dy_1//dx)/(dy_2//dx)=(e^tan x .sec^2 x )/(cos x)`
`=e^(tan x).sec ^3 x `