Derivative and Gradient

In the introduction, we mentioned Derivative equals to gradient and also slope.

The derivative can be used to find any point-slope in a function.

For example

$f(x)=x^{2}$

Then let’s say we want to know the slope of the point f(4) when $f(x)=x^{2}$

Using derivative $f'(x)=2x$

(you will learn how to do differentiation after this just remember) $f'(x)=2x$ .

so no matter what, when x=4 then f(x) = f(4) = 4^2 = 16

Then using differentiation $f'(x)=2x$ we can solve the slope.

$f'(x)=2*4=8$ so we know that slope will be equal to 8.

When x=8 then $f(x)=64$ then finding the slope of that point on the graph $f'(x)=16$ the slope will be equals to 16.

Finding slope is one way to use differentiation, but there are lots of other ways to use differentiation.