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PROGRAMME 7

This comprehensive guide covers essential differentiation techniques, including standard derivatives, logarithmic differentiation, and implicit functions. Key methods such as the product and quotient rules, as well as handling parametric equations, are outlined with clear examples. Whether you're differentiating simple functions or navigating more complex relationships involving derivatives, this resource provides a structured approach to mastering these concepts. Enhance your calculus skills and apply these techniques in various mathematical scenarios effectively.

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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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