Question

Differentiating Exponential functions In Exercise,find the derivative of the function. See Example 2 and 3.

y = x2ex - 2xex + 2ex

Answer 1

Derivative of the expression will be
`2e^x`

Explanation:

We have given function
`y=x^2e^x-2xe^x+2e^x`

We have to fond the derivative of the expression

Let
`(dy)/(dx)=D_1-D_2+D_3` , here
`D_1=x^2e^x`,
`D_2=2xe^x` and
`D_3=2e^x`

Now first
`D_1=x^2(d)/(dx)e^x+e^x(d)/(dx)x^2=x^2e^x+2xe^x`

`D_2=2[x(d)/(dx)e^x+e^x(d)/(dx)x]=2xe^x+2e^x`

Now
`D_3=2(d)/(dx)e^x=2e^x`

So

`D=x^2e^x+2xe^x-(2xe^x+2e^x)+2e^x=2e^x`