Simple Differentiation

Question

I saw this question and with my basic knowledge of differentiation I don't know what it means. $\frac{d}{dx}(x^2)$ where $x=3$

Where would I start to solve this?

It means: What is the value of the derivative of $y=x^2$ at the point when $x=2$? If you only know derivatives as limits, you are being asked to find $$\lim_{h\to 0}\frac{(3+h)^2 - 3^2}{h}.$$ If you already know the Power Rule, it's asking you to use the general formula for $\frac{d}{dx}(x^2)$, and plug in $x=3$ to get the value of the derivative at the point. Remember that the derivative at a point is just a number (the slope of the tangent to the graph at the point with $x$-coordinate $3$).
@ArturoMagidin In your first sentence, do you mean $x=3$? [I cannot comment and so I had to create an answer]

Emmad Kareem · Answer 1 · 2011-11-14 23:13:11Z

The derivative of a function is related to the concept of the rate of change of a function.

Either you use the method presented by @Arturo Magidin, or you apply a formula.

An example of a formula is for:

$f(x) = x^{n} $

the derivative (denoted by either ${f}'(x)$ or $\frac{d}{dx} f(x)$ is

$ n x^{n-1} $

so in you case (n=2)

$f(x) = x^{2} $ and $\frac{d}{dx}f(x)= 2 x^{2-1} = 2x$

at point x=3

${f}'(3) = 2*3 = 6$

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