Differentiation Lesson 1

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DifferentiationLesson 1

• Chapter 7

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We need to be able to find the gradient of a
straight line joining two points
Find the gradient of the line joining (4, -11)
and (-2, 7)
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Describe the way the gradient is changing on
these graphs
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Finding the gradient of a curve

• (differentiation)

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How can you find the gradient of a curve if it
keeps changing??
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E.g. the function y x2
Go to GSP file
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The ideal way to find a gradient of a curve is to
find the gradient of the tangent at the point we
are interested in
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Finding the gradient

• The process of finding the gradient of a curve is
  called differentiation
• You can differentiate any function to find its
  gradient

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In general it can be shown that

• If f(x) xn where n is a real number
• Then
• f (x) nxn-1

f(x) xn
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In general it can be shown that
f(x) xn
f (x) nxn-1
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In other words
f(x) xn f (x) nxn-1
E.g. 1
-1
1) Multiply function by power of x 2) Subtract 1
from the power
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In other words
f(x) xn f (x) nxn-1
E.g. 1
1) Multiply function by power of x 2) Subtract 1
from the power
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Notation
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Now do Ex 7B on page 109