Question

second order derivative of e^2x multipled by tanx​

Answer 1

Answer:

2 e^2x . sec² x . tan x + 4 e^2x . sec² x + 4 e^2x . tan x

Step-by-step explanation:

Given :

f ( x ) = e^2x . tan x

We are asked to find second order derivative i.e. y₂ :

Using product rule :

d / d x ( u v ) = u ( v )' + v ( u )'

y₁ = e^2x ( tan x )' + tan x ( e^2x )

= > y₁ = e^2x . sec² x + 2 e^2x . tan x

Now :

= > y₂ = e^2x ( sec² x )' + sec² x ( e^2x )' + 2 [ e^2x ( tan x ) + tan x ( e^2x )' ]

= > y₂ = 2 e^2x . sec² x . tan x + 2 e^2x . sec² x + 2 [ e^2x . sec² x + 2 e^2x . tan x ]

= > y₂ = 2 e^2x . sec² x . tan x + 4 e^2x . sec² x + 4 e^2x . tan x

Hence we get required answer!