Derivative

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Derivative

• Part 2

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Definition

• The derivative of a function f is another
  function f (read f prime) whose value at any
  number x is
• Provided that this limit exists and is not ? or -?

• If this limit does exist ? f differentiable at c
• Other way ? if f differentiable at x1 then f
  (x1) exist
• If a function differentiable at every riil number
  in their domain then f called differentiable
  function

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Soo

• if x1 belong to domain then

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Add

• Note
• If we take
• then

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Differentiability Implies Continiuty
Ex. Check if continue at x0 and differentiable
at x0?
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The Constant Rule
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The Power Rule
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The Constant Multiple Rule
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The Sum and Difference Rules
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Derivatives of Sine and Cosine Functions
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The Product Rule
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The Quotient Rule
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Derivatives of Trigonometric Function
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Leibniz Notation for Derivatives
Ultimately, this notation is a better and more
effective notation for working with derivatives.
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Teorema

• If and differentiable function
  then

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The Chain Rule
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The General Power Rule
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Summary of Differentiation Rules
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Exercise 1
Suppose f with Find a and b such as f
continue at x0 but f(0) doesnt exist
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Exercise 2
Check if the function differentiable at 0 ??
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Ex3
Check if the function Differentiable at
x0
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Ex 4
Find the derivative from the function
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Ex 5
Calculate d/dx(?x?) then show the function y ?x?
satisfied yyx, x?0
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Ex 6

• Find the derivative from the invers function