Question

use the product rule to find the derivative.
y=(5x^2 + 3)(2x - 5)
y=□

Explanation:

Step1: Recall product - rule

The product rule states that if $y = u\cdot v$, then $y'=u'v + uv'$. Let $u = 5x^{2}+3$ and $v = 2x - 5$.

Step2: Find $u'$

Differentiate $u = 5x^{2}+3$ with respect to $x$. Using the power - rule $\frac{d}{dx}(ax^{n})=nax^{n - 1}$, we have $u'=\frac{d}{dx}(5x^{2}+3)=10x$.

Step3: Find $v'$

Differentiate $v = 2x - 5$ with respect to $x$. Using the power - rule, $v'=\frac{d}{dx}(2x - 5)=2$.

Step4: Apply product - rule

Substitute $u$, $u'$, $v$, and $v'$ into the product rule formula:

$$
LATEXBLOCK0
$$

Answer:

$30x^{2}-50x + 6$