Use the product rule to find the derivative of $$ \left(-8 x^{6}-7 x^{5}\right)\left(9 e^{x}-8\right) $$ Use $$ e^{\wedge} x $$ for $$ e^{x} $$. You do not need to expand out your answer.

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To find the derivative of the function

$$
y = \left(-8 x^{6}-7 x^{5}\right)\left(9 e^{\wedge} x - 8\right),
$$

we will use the product rule, which states that if $$ u $$ and $$ v $$ are functions of $$ x $$, then the derivative of their product is given by

$$
(uv)' = u'v + uv'.
$$

Let

$$
u = -8 x^{6} - 7 x^{5}
$$
and 
$$
v = 9 e^{\wedge} x - 8.
$$

First, we need to find the derivatives $$ u' $$ and $$ v' $$.

1. **Finding $$ u' $$**:

$$
u' = \frac{d}{dx}(-8 x^{6}) + \frac{d}{dx}(-7 x^{5}) = -48 x^{5} - 35 x^{4}.
$$

2. **Finding $$ v' $$**:

$$
v' = \frac{d}{dx}(9 e^{\wedge} x) + \frac{d}{dx}(-8) = 9 e^{\wedge} x.
$$

Now we can apply the product rule:

$$
y' = u'v + uv'.
$$

Substituting $$ u $$, $$ u' $$, $$ v $$, and $$ v' $$ into the product rule gives:

$$
y' = (-48 x^{5} - 35 x^{4})(9 e^{\wedge} x - 8) + (-8 x^{6} - 7 x^{5})(9 e^{\wedge} x).
$$

Thus, the derivative of the given function is

$$
\boxed{(-48 x^{5} - 35 x^{4})(9 e^{\wedge} x - 8) + (-8 x^{6} - 7 x^{5})(9 e^{\wedge} x)}.
$$
The derivative of the given function is $$ (-48 x^{5} - 35 x^{4})(9 e^{\wedge} x - 8) + (-8 x^{6} - 7 x^{5})(9 e^{\wedge} x). $$

Use the product rule to find the derivative of \[ \left(-8 x^{6}-7 x^{5}\right)\left(9 e^{x}-8\right) \] Use \( e^{\wedge} x \) for \( e^{x} \). You do not need to expand out your answer.

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