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Published byGabriel Russell Modified over 3 years ago

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Differentiation Revision for IB SL

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Type of function Rule used to differentiate Polynomial Constant Always becomes zero Remember that, e, ln(3), are still constants Composite function (function of a function) Chain rule

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Type of function Rule used to differentiate 2 functions of x multiplied together Product rule 1 function of x divided by another function of x Quotient rule Exponential function

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Type of function Rule used to differentiate Natural logarithm Trigonometric functions

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Chain Rule

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Product Rule

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Quotient Rule

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exexexex

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ln(x)

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Trigonometric functions

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Find gradient at particular point Substitute the x-value for that point into the expression for dy/dx. Substitute the x-value for that point into the expression for dy/dx. With implicit functions, you will need the x and y values. With implicit functions, you will need the x and y values.

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Find tangent or normal A tangent or normal is a straight line (y = mx + c). A tangent or normal is a straight line (y = mx + c). For the tangent, m is the gradient at that point. For the tangent, m is the gradient at that point. For the normal, m is For the normal, m is

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Find turning points and their nature (min/max) Turning pt is when dy/dx=0 Turning pt is when dy/dx=0 To determine nature: To determine nature: 1.Use 2 nd derivative test If d 2 y/dx 2 : –> 0, local minimum –< 0, local maximum –= 0, test inconclusive – could be min, max or point of inflection 2.Examine gradient on either side of the point. Use this method if finding the 2 nd derivative is too hard or if the test was inconclusive.

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Find turning points and their nature (min/max)

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Points of inflection A point of inflection is the point on a curve when it changes from concave- up to concave-down, or vice-versa. A point of inflection is the point on a curve when it changes from concave- up to concave-down, or vice-versa. This is the point when the second derivative, d 2 y/dx 2, equals zero

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Summary

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Motion of particles s, displacement s, displacement v, velocity v, velocity a, acceleration a, acceleration E.g. what is the velocity function for a particle if its displacement function is E.g. what is the velocity function for a particle if its displacement function is s = (3x-2) 4 Differentiate

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