find the derivative of the function
$g(x)=(x^{2}+x - 1)e^{x}$
$g(x)=$
note: you are in the reduced scoring period. all work counts for 85% of the original.
preview my answers submit answers
your score was recorded.
scores are sent to d2l brightspace every 24 hours.
you have attempted this problem 3 times.
you received a score of 0% for this attempt.
your overall recorded score is 0%.
you have unlimited attempts remaining.

Question

Accepted Answer

# Explanation:
## Step1: Apply the product rule
The product rule states that if $y = f(x)g(x)$, then $y^\prime=f^\prime(x)g(x)+f(x)g^\prime(x)$. Let $f(x)=x^{2}+x - 1$ and $g(x)=e^{x}$. First, find $f^\prime(x)$:
$$
\begin{align*}
f^\prime(x)&=\frac{d}{dx}(x^{2}+x - 1)\
&=\frac{d}{dx}(x^{2})+\frac{d}{dx}(x)-\frac{d}{dx}(1)\
&=2x + 1-0\
&=2x+1
\end{align*}
$$
And $g^\prime(x)=\frac{d}{dx}(e^{x})=e^{x}$

## Step2: Substitute into the product rule formula
$$
\begin{align*}
g^\prime(x)&=(2x + 1)e^{x}+(x^{2}+x - 1)e^{x}\
&=e^{x}[(2x + 1)+(x^{2}+x - 1)]\
&=e^{x}(2x + 1+x^{2}+x - 1)\
&=e^{x}(x^{2}+3x)
\end{align*}
$$

# Answer:
$g^\prime(x)=e^{x}(x^{2}+3x)$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Apply the product rule

Step2: Substitute into the product rule formula

Answer: