use the product rule to find the derivative. y=(5x^2 + 2)(4x - 5) y=

Explanation:

Step1: Identify functions u and v

Let $u = 5x^{2}+2$ and $v = 4x - 5$.

Step2: Find u' and v'

Differentiate $u$ with respect to $x$: $u'=\frac{d}{dx}(5x^{2}+2)=10x$. Differentiate $v$ with respect to $x$: $v'=\frac{d}{dx}(4x - 5)=4$.

Step3: Apply product - rule

The product - rule states that $(uv)'=u'v + uv'$. Substitute $u$, $v$, $u'$, and $v'$ into the formula: $y'=(10x)(4x - 5)+(5x^{2}+2)\times4$.

Step4: Expand and simplify

First, expand $(10x)(4x - 5)=40x^{2}-50x$ and $(5x^{2}+2)\times4 = 20x^{2}+8$. Then $y'=40x^{2}-50x + 20x^{2}+8$. Combine like - terms: $y'=(40x^{2}+20x^{2})-50x + 8=60x^{2}-50x + 8$.

Answer:

$60x^{2}-50x + 8$