Differentiating using First Principals

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Differentiating using First Principals
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To find the gradient of a tangent at the point A
Equation of the tangent takes the form y mx
c m is the gradient of the tangent
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1. Start with a chord of length AB2. B moves
towards A.3. When B reaches C the chord is
getting shorter and closer to A
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Gradient AB
B
f(xh)
A
f(x)
h
x
xh
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Example Find the gradient of the tangent at any
point x
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Example Find the gradient of the tangent at any
point x
Substituting
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Example Find the gradient of the tangent at any
point x
Multiply out the brackets
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Example Find the gradient of the tangent at any
point x
Divide top and bottom by h
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Example Find the gradient of the tangent at any
point x
h becomes 0
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Note
Differentiated gives
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Practice Differentiate from first principals
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Worksheet 1