Question

$$\frac { d } { d x } ( 2 x + 1 ) ( 5 x - 4 ) $$

Explanation:

Step1: Apply the product rule

The product rule states that if \(y = u\cdot v\), then \(y^\prime=u^\prime v + uv^\prime\). Let \(u = 2x + 1\) and \(v=5x - 4\). First, find \(u^\prime\) and \(v^\prime\).
\(u^\prime=\frac{d}{dx}(2x + 1)=2\) and \(v^\prime=\frac{d}{dx}(5x - 4)=5\)

Step2: Substitute into the product rule formula

\(\frac{d}{dx}[(2x + 1)(5x - 4)]=(2x + 1)\times5+(5x - 4)\times2\)

Step3: Expand the expressions

\((2x + 1)\times5 = 10x+5\) and \((5x - 4)\times2=10x - 8\)

Step4: Combine like - terms

\((10x + 5)+(10x - 8)=10x+10x+5 - 8=20x - 3\)

Answer:

\(20x - 3\) (the option in the green box)