Introduction to :

Things to remember for implicit differentiation:

  • x' = 1
  • since y is a function of x, any derivative involving y must use the chain rule
      
  • since y is a function of x, taking the derivative of xy (or of any other product involving both x and y) requires the product rule
      
  • since y is a function of x, taking the derivative of  (or any other quotient involving both x and y) requires the quotient rule

Practice:

Example 1

If y is a function of x and

x2 + y2 = 16,

find y'.


Example 2

Find y' given that y is a function of x and xy + x2 + y2 = 0.


Exercise 1

Use implicit differentiation to find y', assuming in the case that y is a function of x.

  • x3 + y3 = 4x

Exercise 2

Use implicit differentiation to find y', assuming in the case that y is a function of x.

  • y = cos(y) + 2x

Exercise 3

implicit differentiation to find y', assuming in the case that y is a function of x.

  •  e{y2} - x = y

Exercise 4

implicit differentiation to find y', assuming in the case that y is a function of x.

  • xy2 + x3y = 4x

Exercise 5

implicit differentiation to find y', assuming in the case that y is a function of x


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