Question

How do you differentiate `f(x)=(2e^x+x)(x-2)` using the product rule?

Answer 1

`2e^x + x + (x-2)(2e^x + 1)`

Explanation:

Differentiate using the `color(blue)" product rule "`

If f(x) = g(x).h(x) then f'(x) = g(x).h'(x) + h(x).g'(x)

the standard derivative : `d/dx(e^x) = e^x`
`" ----------------------------------------------------"`

g(x) = `2e^x + x rArr g'(x) = 2e^x + 1`

and h(x) = x - 2 `rArr h'(x) = 1`
`" -------------------------------------------------"`

Substituting these values into f'(x)

`rArr f'(x) = 2e^x + x + (x-2)(2e^x + 1)`