Question

The derivative of f(x)=3x^2+2x+4 w.r.t to x is

Answer 1

Explanation is written in the image linked above.

Answer 2

Answer:

The derivative of the function is $6 x+2$

Explanation:

The derivative of a function $y = f(x)$of a variable $x$ is a measurement of the rate at which the function's value $y$changes when the variable $x$varies.

The velocity of a moving item is the derivative of its position over time. It assesses how quickly an object or person's position changes as time passes.

Given: $y=f(x)=3 x^{2}+2 x+4$

Now differentiate wrt $x$

$\frac{d y}{d x}=\frac{d}{d x}\left(3 x^{2}+2 x+4\right)$

$\begin{aligned}&\frac{d y}{d x}=\frac{d}{d x}\left(3 x^{2}\right)+\frac{d(2 x)}{d x}+\frac{d}{d x}(4) \\&\frac{d y}{d x}=2 \times 3 x^{2-1}+2 \times 1 x^{-1}+0\end{aligned}$

$f^{\prime}(x)=\frac{d y}{d x}=6 x+2$

The derivative of the function is $6 x+2$.