Implicit derivation

Examples:

1)

 

2) Find the tangent line to the hyperbola x2 – y2 = 16 at the point (5,3)

 

 

Exercises:

1.- Find the derivative of these functions:

a) x·y = 4

b) x2 - y3 = 0

 

2.- Let the circumference x2 + y2 = 52

a) Find the tangent to the circumference at the point (3,4).

b) Find the horizontal tangents to the circumference.

 

 

 

 

Solutions:

1.- a) y' = -4/x2; b) y' = 2x/(33√x4)

2.- a) y - 4 = -3/4 (x - 3); b) y = ±5

 

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