Question

How do you differentiate `f(x)=-xe^x*(4-x)/6` using the product rule?

Answer 1

`f'(x)=(xe^x)/6-(xe^x(4-x))/6-(e^x(4-x))/6`

Explanation:

If a function `f(x)=uvw` where `u`, `v` and `w` are all functions of `x`, then `f'(x)=uvw'+uv'w+u'vw`

`u=-x`
`u'=-1`

`v=e^x`
`v'=e^x`

`w=(4-x)/6=4/6-x/6`
`w'=-1/6`

`f'(x)=(xe^x)/6-(xe^x(4-x))/6-(e^x(4-x))/6`