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Презентация на тему по математике Правила дифференцирования, 10 класс

The gradient of a straight line is given by
Made by ALEXP1 Chapter 6.1«The Rule for Differentiation» The gradient of a straight line is given by 7 - 1 = 6Solution:3 - 1 = 2 The gradient of a straight line is given byWe use this idea The Gradient at a point on a CurveDefinition: The gradient of a The gradient changes as we move along a curvee.g. Point on the curveGradient The notation comes from the idea of the gradient of a line being ddxyThe notation comes from the idea of the gradient of a line being “subtract 1 from the power” “power to the front and multiply”Other curves and their gradient functions Gradient of Summary of Gradient Functions: The Gradient Function and Gradient at a PointAt x = 2, the gradient ExercisesAt  x = - 1,  m = -4Solution:Solution: tangent at x = 1 More Gradient Functions tangent at x = 1 tangent at x = 1 e.g.  The rule can also be used for sums and differences of terms. Solution:Differentiating to find the gradient function: When x = 1, gradient m = Using Gradient Functions SUMMARYThe gradient at a point on a curve is defined as the Find the gradients at the given points on the following curves:Exercises 5.( Multiply out the brackets before using the rule )(Divide out before
Слайды презентации

Слайд 2 The gradient of a straight line is given

The gradient of a straight line is given by

Слайд 3 7 - 1 = 6
Solution:
3 - 1 =

7 - 1 = 6Solution:3 - 1 = 2

Слайд 4 The gradient of a straight line is given

The gradient of a straight line is given byWe use this

by
We use this idea to get the gradient at

a point on a curve

This branch of Mathematics is called Calculus


Слайд 5 The Gradient at a point on a Curve
Definition:

The Gradient at a point on a CurveDefinition: The gradient of

The gradient of a point on a curve equals

the gradient of the tangent at that point.

e.g.

3

12

So, the gradient of the curve at (2, 4) is 4


Слайд 6 The gradient changes as we move along a

The gradient changes as we move along a curvee.g.

curve
e.g.


Слайд 14
Point on the curve
Gradient

Point on the curveGradient

Слайд 15 The notation comes from the idea of the

The notation comes from the idea of the gradient of a line being

gradient of a line being


Слайд 16 d
d
x
y
The notation comes from the idea of the

ddxyThe notation comes from the idea of the gradient of a line being

gradient of a line being


Слайд 17 “subtract 1 from the power”
“power to the

“subtract 1 from the power” “power to the front and multiply”Other curves and their gradient functions

front and multiply”
Other curves and their gradient functions


Слайд 24 Gradient of


Gradient of

Слайд 27 Summary of Gradient Functions:

Summary of Gradient Functions:

Слайд 28 The Gradient Function and Gradient at a Point
At

The Gradient Function and Gradient at a PointAt x = 2, the gradient

x = 2, the gradient


Слайд 29 Exercises
At x = - 1, m

ExercisesAt x = - 1, m = -4Solution:Solution:

= -4
Solution:
Solution:


Слайд 31 tangent at x = 1
More Gradient Functions

tangent at x = 1 More Gradient Functions

Слайд 32 tangent at x = 1
tangent at x

tangent at x = 1 tangent at x = 1

= 1


Слайд 33 e.g.
The rule can also be used

e.g. The rule can also be used for sums and differences of terms.

for sums and differences of terms.


Слайд 34 Solution:
Differentiating to find the gradient function:
When x

Solution:Differentiating to find the gradient function: When x = 1, gradient m = Using Gradient Functions

= 1, gradient m =
Using Gradient Functions


Слайд 35 SUMMARY
The gradient at a point on a curve

SUMMARYThe gradient at a point on a curve is defined as

is defined as the gradient of the tangent at

that point

The process of finding the gradient function is called differentiating

The function that gives the gradient of a curve at any point is called the gradient function

The rule for differentiating terms of the form


Слайд 36 Find the gradients at the given points on

Find the gradients at the given points on the following curves:Exercises

the following curves:
Exercises


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