Travis Fogle

2021-11-19

Find the derivative of $f\left(x\right)={x}^{2}+3x$ at x. That is, find f′(x).

Harr1957

Beginner2021-11-20Added 18 answers

Step 1

We have to find the derivative of f(x) at x :

$f\left(x\right)={x}^{2}+3x$

We will use following formula, for derivatives,

$\frac{df\left(x\right)}{dx}={f}^{\prime}\left(x\right)$

$\frac{da{x}^{n}}{dx}=an{x}^{n-1}$

$\frac{dx}{dx}=1$

Step 2

So finding derivative with respect to 'x', we get

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

$f}^{\prime}\left(x\right)=\frac{{dx}^{2}}{dx}+3\frac{dx}{dx$

$=2{x}^{2-1}+3\times 1$

=2x+3

Hence, value of f'(x) is 2x+3.

We have to find the derivative of f(x) at x :

We will use following formula, for derivatives,

Step 2

So finding derivative with respect to 'x', we get

=2x+3

Hence, value of f'(x) is 2x+3.