# Formal definition of derivatives a short explanation

*Note: I’m trying something new, while I’m learning new concepts, I will try to use the Feynman technique to cement my learning and share the explanations with you. Hopefully, some of these explanations can prove helpful in your learning journey.*

We can turn derivatives into limits.

Here we have an example graph:

Before finding the slope of *a*. We can work out the slope of the general function. The plot *x *and *x + h*.

*h *is an arbitrary small number that can be adjusted as *h *approaches 0.

2 x’s cancel out in the numerator.

As *h* approaches zero to get the slope we can write:

Which equals *f’(x)*the derivative of *f(x)*.

Now we can use the *a *point from earlier. We can work out the derivative of *a* by just plugging in the point.

Now we have made a tangent line when *x=a*.

Now what happens if you don’t care about slope of the function and you only care about getting one point?

You can use an alternative form below:

In visual form:

As we can see we have a tangent line between* a* and *x*.

instead of *h* getting smaller we have *x* getting smaller and getting closer to a.