2. -/1 points details my notes differentiate the function. h(x) = (x - 5)(5x + 23) h(x) = need help? read it…
2. -/1 points details my notes differentiate the function. h(x) = (x - 5)(5x + 23) h(x) = need help? read it watch it
Answer
Explanation:
Step1: Use product - rule
The product - rule states that if $h(x)=f(x)g(x)$, then $h'(x)=f'(x)g(x)+f(x)g'(x)$. Here, let $f(x)=x - 5$ and $g(x)=5x + 23$.
Step2: Find $f'(x)$ and $g'(x)$
Differentiate $f(x)$: $f'(x)=\frac{d}{dx}(x - 5)=1$. Differentiate $g(x)$: $g'(x)=\frac{d}{dx}(5x + 23)=5$.
Step3: Apply the product - rule
$h'(x)=f'(x)g(x)+f(x)g'(x)=1\times(5x + 23)+(x - 5)\times5$.
Step4: Simplify the expression
[ \begin{align*} h'(x)&=5x+23 + 5x-25\ &=(5x + 5x)+(23 - 25)\ &=10x-2 \end{align*} ]
Answer:
$10x - 2$