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PROGRAMME 7

PROGRAMME 7. DIFFERENTIATION. Programme 7: Differentiation. Standard derivatives Functions of a function Logarithmic differentiation Implicit functions Parametric equations. Programme 7: Differentiation. Standard derivatives Functions of a function Logarithmic differentiation

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PROGRAMME 7

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  1. PROGRAMME 7 DIFFERENTIATION

  2. Programme 7: Differentiation Standard derivatives Functions of a function Logarithmic differentiation Implicit functions Parametric equations

  3. Programme 7: Differentiation Standard derivatives Functions of a function Logarithmic differentiation Implicit functions Parametric equations

  4. Programme 7: Differentiation Standard derivatives As an aide memoir this slide and the following slide contain the list of standard derivatives which should be familiar.

  5. Programme 7: Differentiation Standard derivatives

  6. Programme 7: Differentiation Standard derivatives Functions of a function Logarithmic differentiation Implicit functions Parametric equations

  7. Programme 7: Differentiation Functions of a function If: then For example:

  8. Programme 7: Differentiation Functions of a function If: then For example:

  9. Programme 7: Differentiation Functions of a function Products Quotients

  10. Programme 7: Differentiation Functions of a function Products If: then For example:

  11. Programme 7: Differentiation Functions of a function Quotients If: then For example:

  12. Programme 7: Differentiation Standard derivatives Functions of a function Logarithmic differentiation Implicit functions Parametric equations

  13. Programme 7: Differentiation Logarithmic differentiation Taking logs before differentiating may simplify the working. For example: Therefore:

  14. Programme 7: Differentiation Standard derivatives Functions of a function Logarithmic differentiation Implicit functions Parametric equations

  15. Programme 7: Differentiation Implicit functions There are times when the relationship between x and y is more involved and y cannot be simply found in terms of x. For example: In this case a relationship of the form y = f (x) is implied in the given equation.

  16. Programme 7: Differentiation Implicit functions To differentiate an implicit function remember that y is a function of x. For example, given: Differentiating throughout gives: so.

  17. Programme 7: Differentiation Standard derivatives Functions of a function Logarithmic differentiation Implicit functions Parametric equations

  18. Programme 7: Differentiation Parametric equations Sometimes the relationship between x and y is given via a third variable called a parameter. For example, from the two parametric equations the derivative of y with respect to x is found as follows:

  19. Programme 7: Differentiation Parametric equations The second derivative is found as follows:

  20. Programme 7: Differentiation Learning outcomes • Differentiate by using a list of standard derivatives • Apply the chain rule • Apply the product and quotient rules • Perform logarithmic differentiation • Differentiate implicit functions • Differentiate parametric equations

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