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Calc

Differentiation

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Calc

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  1. A formal method of finding a gradient function. y average gradient… f(x+h)-f(x) h x x+h x

  2. y f(x+h)-f(x) h x x+h x

  3. y f(x+h)-f(x) h x x x+h

  4. y f(x+h)-f(x) h x x x+h

  5. y f(x+h)-f(x) h x x x+h

  6. y f(x+h)-f(x) h x x x+h

  7. y f(x+h)-f(x) h x x x+h

  8. y f(x+h)-f(x) h x x x+h

  9. y x x x+h

  10. y x x x+h

  11. y instantaneous gradient at x x x:x+h

  12. As h→0, the average gradient approaches the actual gradient at x Gradient at x As This leads to the formal definition of the derivative

  13. Definition: The function f‘(x) defined by: is called the derivative of f with respect to x – or the gradient function of f(x). Using the definition to find the gradient function (or derivative) of f, is sometimes referred to as “…finding the gradient/derivative using First Principles” Let’s use it to find some other gradient functions….

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