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Leibniz Notation

Leibniz Notation. Liebniz Notation is an alternative way of expressing derivatives to f'(x) , g'(x) , etc. If y is expressed in terms of x then the derivative is written as dy / dx. eg y = 3x 2 - 7x. so dy / dx = 6x - 7. Example 22. Q = 9R 2 - 15 R 3.

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Leibniz Notation

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  1. Leibniz Notation Liebniz Notation is an alternative way of expressing derivatives to f'(x) , g'(x) , etc. If y is expressed in terms of x then the derivative is written as dy/dx . eg y = 3x2 - 7x so dy/dx = 6x - 7 . Example 22 Q = 9R2 - 15 R3 Find dQ/dR ! NB: Q = 9R2 - 15R-3 So dQ/dR = 18R + 45R-4 = 18R + 45 R4

  2. Example 23 A curve has equation y = 5x3 - 4x2 + 7 . Find the gradient where x = -2 ! gradient = dy/dx = 15x2 - 8x if x = -2 then gradient = 15 X (-2)2 - 8 X (-2) = 60 - (-16) = 76

  3. Extra bit for “FIZZY SYSTS” or even Physicists. Newton’s 2ndLaw of Motion s = ut + 1/2at2 where s = distance & t = time. Finding ds/dt gives us a “diff in dist”  “diff in time” ie speed or velocity so ds/dt = u + at but ds/dt = v so we get v = u + at and this is Newton’s 1st Law of Motion

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