Differentiation in Core 1 :)

This is a powerpoint presentation I made on differentiation. I had to teach this topic to an A level class before I had actually learnt it myself, and this was the resource that I used to aid my learning, and help describe the basic termonolgy and ideas behind differentiation.

I hope you find it useful :)

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  • Created by: George
  • Created on: 10-05-11 17:35
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What is differentiation
Differentiation is the process which allows us
to find the rates of change (derivatives).
Differentiating allows us to find the rate of
change of x with respect to y.
Example
Differentiation allows us to find the rate of
change of velocity with respect to time, which
is . . . . . acceleration…read more

Slide 3

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Calculating an estimate of the
gradient of a line
The gradient of a curve at a specific point is
defined as being the same as the gradient of
the tangent to the curve at that point
y = f(x)
A
Tangent at point
A…read more

Slide 4

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Finding the formula for the
n
gradient of a function f(x) = x
How would you go about finding the gradient of
the chord from point B to point C?
(x + h, (x + h)2)
C
Chord Hint
(x,
Change in
x2)B y
Change in
x…read more

Slide 5

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Finding the formula for the
n
gradient of a function f(x) = x
The gradient of the chord from B to C is:
2x + h
By limiting the value of h, the gradient of the
chord becomes closer to the tangent to the
curve at point B
Gradient of the tangent is therefore 2x…read more

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Notations
The differentiated term can be written as:
dy / dx or f `(x)
dy / dx means differentiating y with respect to x
Second order derivative is written as::
d2y / dx2 or f''(x)…read more

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