Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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 $3$). – Arturo Magidin Nov 14 '11 at 20:56
@ArturoMagidin In your first sentence, do you mean $x=3$? [I cannot comment and so I had to create an answer] – psp Nov 14 '11 at 21:17
@psp: Good catch! Yes. – Arturo Magidin Nov 14 '11 at 21:41

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

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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.