can't understand derviatives from searching all over the internet

Question

I have tried to follow a lot of tutorials out there for explaining derviatives and show (understandable)examples but i couldn't understand any. Can anyone link me a useful and easy to follow tutorial or explain derviatives for me?

Answer 1

I would highly recommend watching 3blue1brown's series on calculus. If you're having trouble grasping the intuition behind derivatives, then his animation style definitely helps out. He has a clear geometric representations on different topics. Just remember that although his videos are very useful for intuition, it's more qualitative than quantative. Be sure to explore the topics even further on your own and do practice questions.

Answer 2

https://www.youtube.com/watch?v=N2PpRnFqnqY

Khan Academy is a great resource if you want to learn math online. It also has a wide selection of calculus tutorials that are all narrated and explained very well.

I will try to explain what a derivative is in a nutshell: it is the slope of a line at a point. For example, the derivative of the function $f(x) = x^2$ is $f'(x) = 2x$. (the apostrophe, or 'prime' is just convention for derivatives.) You will notice that for $x = 1$, the slope of the tangent line is $2x$ or $2(1)$. (You will also have to change the y intercept). Observe the image:

parabola image

Answer 3

Let me give you a very simple one.

lets say you want to find out the derivative of $$3x^2$$

You bring down the exponent which is 2 and multiply it by 3, just like this.

2*3x

and then you subtract that exponent by 1.

so it should look like this: $n*(3x^{n-1})$

therefore the answer would be 6x. There's other rules and etc, however this is just a basic idea and concept of it.