Difference between revisions of "Derivative and Gradient"

Latest revision as of 02:23, 26 September 2021

In Derivative you will see $f(x)$ and $f'(x)$

To start the calculus you need to know they are differen't

$f(x)\neq f'(x)$

f(x) = "f" of "x"

f'(x) = derivative of f(x)

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.

@@ Line 1: / Line 1: @@
-In the introduction we have talk about Derivative is equal to gradient and also slop.
+In Derivative you will see
+<math>f(x)</math> and <math>f'(x)</math>
-Derivative can be used to find any point slope in a function
+To start the calculus you need to know they are differen't
+<math>f(x) \neq f'(x)</math>
+f(x) = "f" of "x"
+f'(x) = derivative of f(x)
+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
-<math>f(x)=X^2<\math>
+<math>f(x)=x^2</math>
+Then let’s say we want to know the slope of the point  f(4)
+when <math>f(x)=x^2</math>
+Using derivative
+<math>f'(x)=2x</math>
+(you will learn how to do differentiation after this just remember) <math>f'(x)=2x </math> .
+so no matter what, when x=4 then f(x) = f(4) = 4^2 = 16
+Then using differentiation <math>f'(x)=2x </math> we can solve the slope.
+<math>f'(x)= 2*4 = 8</math>
+so we know that slope will be equal to 8.
+When x=8 then <math>f(x)=64</math> then finding the slope of that point on the graph <math>f'(x)=16</math> 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.