Question

y = - 2x + 5
find derivative

Explanation:

Step1: Apply derivative rules

$$\frac{dy}{dx}=\frac{d(-2x + 5)}{dx}$$

Step2: Use sum rule of derivatives

$$\frac{dy}{dx}=\frac{d(-2x)}{dx}+\frac{d(5)}{dx}$$

Step3: Apply power rule ($\frac{d(x^n)}{dx}=nx^{n - 1}$) and constant rule ($\frac{d(c)}{dx}=0$, $c$ is constant)

For $y=-2x+5$, when $n = 1$ for the term $-2x$ and $c = 5$ for the constant term.
$$\frac{d(-2x)}{dx}=-2\times1\times x^{1 - 1}=-2$$, $$\frac{d(5)}{dx}=0$$

Step4: Combine results

$$\frac{dy}{dx}=-2+0$$

Answer:

$-2$