2'7 Implicit Differentiation

1
2.7 Implicit Differentiation
2
Explicit versus Implicit

• Explicit form
• yf(x)
• Example yf(x)x2
• Implicit form
• f(x,y)c
• Example xy5

3
Implicit Differentiation

• Must understand and apply the Chain Rule
• The equation will not be expressed as
• yf(x)
• But you must think that it is.
• Example
• y2x
• This is the same as f(x)2x
• Differentiate both sides
• 2 f(x)f ? (x) 1
• 2yy ? 1
• y ? 1/2y

4
Procedure

• Differentiate both sides of the equation with
  respect to x
• Write the result so that all terms containing y ?
  (or dy/dx) are on the left side and other terms
  are on the right
• Factor out y ? (or dy/dx) on the left
• Divide both sides by the factor of y ?(or dy/dx)

5
http//www.howardcc.edu/math/MA145/2.7/2.7.htm