Does anyone want to explain derivatives? I want to learn them over the summer and I don't know where to start!

Question

zzr0ck3r · Answer

Read any calculus book.

zzr0ck3r · Answer

In short, the derivative of a function evaluated at $x$ is the slope of the curve at $x$.

zzr0ck3r · Answer

So just like you have a way to find the slope of a line in the form $y=mx+b$, we can generalize to find the slope of 'any' curve.

jh99 · Answer

I've already watched several videos... I can't grasp onto the concept of derivatives

zzr0ck3r · Answer

which part?

jh99 · Answer

"The derivative of a function of a real variable measures the sensitivity to change of a quantity which is determined by another quantity (the independent variable)." -Wikipedia

geerky42 · Answer

Have you tried Khan Academy? https://www.khanacademy.org/math/calculus-home/

kinged · Answer

Derivatives are a trick that uses limits. If you understand limits, then you'll know how to get the slope of a curve at point (that's when the denominator as in "Rise over Run" reaches zero.)

campbell_st · Answer

Just remember that the derivative gives the rate of change in one variable with respect to a 2nd variable.

if you had an equation 

$$y = x^2$$    the average rate of change in y with respect to x between x the points (0,0) and (2, 4) can be found by finding the slope of the line segment joining the points.  Which will be an approximation.

by taking the derivative you are finding the instantaneous rate at a specific point. No need to 2 points. 

hope it helps

kinged · Answer

Watch this from MIT: https://www.youtube.com/watch?v=UcWsDwg1XwM

mww · Answer

They aren't that tricky but it does take a bit of time to get your head around.
Quick tutorial:

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mww · Answer

You can draw a line joining P and Q, known as a secant line.

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The average change from point P to point Q is the slope of this secant line
$$m_{PQ} = \frac{ y_2-y_1 }{ x_2-x_1 }=\frac{ f(x+h)-f(x) }{ x+h - x } = \frac{ f(x+h)-f(x) }{ h }$$

Now imagine that you wanted to find the exact (sometimes referred to as instantaneous) rate of change of f with respect to x at the point P. To achieve this, you'd make the difference between P to Q smaller and smaller. In other words you'd calculate the average rate of change, or slope over a shorter distance in x. This can be achieved by dragging Q 'closer' to P.

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