kinda stupid question: if first derivative for x^2 is a slope of a tangent line in any given point of the curve (x^2), what is the first derivative of x^3?

Question

satellite73 · Answer

same thing, only for the point $(x,x^3)$ instead of $(x, x^2)$

ar43r · Answer

I wonder if the slope in x=3 for x^3 would be 18 or 27

photon336 · Answer

Here's the general rule for taking the derivative, i.e power rule 

$$\frac{ d }{ dx } x^{n} = nx^{n-1}$$


you would just take the first derivative of x^3

ar43r · Answer

jepp. and the first derivative of x^3 is 3x^2. which is a parabola.. I was wondering how to find a slope of x^3 in any given point x

photon336 · Answer

the derivative is just a technical way of saying slope :

sweetburger · Answer

Say you want to find the slope of a line of x^3 at any given point. Take the first derivative which nets you 3x^2. Slope = 3x^2. To find the slope at any point on the graph of x^3 plug in the x value into the first derivative this will give you the slope of the line at that specific point.

ar43r · Answer

well I see it now. the slope is a number like for 3x the slope is 3 for any point x.
and for x^2 the slope of x=3 is 6, so the slope of x^3 x=3 must be much steeper than in x^2. 
thanks you all!