Travis Fogle

2021-11-19

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

Harr1957

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
$\frac{df\left(x\right)}{dx}=\frac{d\left({x}^{2}+3x\right)}{dx}$
${f}^{\prime }\left(x\right)=\frac{{dx}^{2}}{dx}+3\frac{dx}{dx}$
$=2{x}^{2-1}+3×1$
=2x+3
Hence, value of f'(x) is 2x+3.

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