# How do you differentiate g(x) =(2x+2)e^(3-x)  using the product rule?

Mar 12, 2018

Derivatie of $g \left(x\right) = \left(2 x + 2\right) {e}^{3 - x}$ is $- 2 x {e}^{3 - x}$

#### Explanation:

Product rule states that derivative of a product of two functions is equal to first function multiplied by derivative of second function plus second function multiplied by derivative of first function.

Here $g \left(x\right) = \left(2 x + 2\right) {e}^{3 - x}$ and while first function is $2 x + 2$, whosederivative is $2$, second function is ${e}^{3 - x}$ and its derivative is $- {e}^{3 - x}$.

and therefore $\frac{\mathrm{dg}}{\mathrm{dx}} = 2 \times {e}^{3 - x} + \left(2 x + 2\right) \left(- {e}^{3 - x}\right)$

= ${e}^{3 - x} \left(2 - 2 x - 2\right)$

= $- 2 x {e}^{3 - x}$