Derivative of a linear function

Question

I have to find the coefficients for m and n in the following linear function $() = + $ the tangent goes through the points $(1,-3)$ then $(1) = + = −3$ and then this comes up $′() = 4 − 3$ I understand that this is a derivative, but I don't remember any formula where this $(4x)$ comes from so my question is what is this $4x$? The quadratic function is f(x) = 2x ² -3x - 2

Answer 1

Since $$\frac{\mathrm{d}}{\mathrm{d}x} x^n = n x^{n-1}$$

$\forall n \in \mathbb{R}$ then

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^2-3x-2)= 2(2x)-3=4x-3$$