Difference between revisions of "Derivative and Gradient"
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In Derivative you will see | |||
<math>f(x)</math> and <math>f'(x)</math> | |||
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. | In the introduction, we mentioned Derivative equals to gradient and also slope. | ||
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For example | 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 | Then let’s say we want to know the slope of the point f(4) | ||
when <math>f(x)=x^2</math> | when <math>f(x)=x^2</math> | ||
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<math>f'(x)=2x</math> | <math>f'(x)=2x</math> | ||
you will learn how do | (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. | 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 | Finding slope is one way to use differentiation, but there are lots of other ways to use differentiation. | ||
Latest revision as of 02:23, 26 September 2021
In Derivative you will see and
To start the calculus you need to know they are differen't
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
Then let’s say we want to know the slope of the point f(4) when
Using derivative
(you will learn how to do differentiation after this just remember) .
so no matter what, when x=4 then f(x) = f(4) = 4^2 = 16
Then using differentiation we can solve the slope.
so we know that slope will be equal to 8.
When x=8 then then finding the slope of that point on the graph 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.