Question

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

y = xex - 4e - x

Answer 1

Answer: The derivative would be
`y'=e^x(1+x)+4e^(-x)`

Explanation:

Since we have given that

`y=xe^x-4e^(-x)`

as we know the product rule:

`xe^x=x'e^x+xe^x'=e^x+xe^x`

so, it becomes,

`y'=e^x(1+x)-4* -1e^(-x)\\\\y'=e^x(1+x)+4e^(-x)`

Hence, the derivative would be

`y'=e^x(1+x)+4e^(-x)`