##
Implicit Differentiation - Exercise 2

**Exercise 2.** Prove that an equation of the tangent line to
the graph of the hyperbola

at the point
*P*(*x*_{0},*y*_{0}) is

**Answer.** Instead of finding *y* explicitly as a function of
*x*, we will use implicit differentiation to find the slope of
the tangent line. We have

or equivalently

So the equation of the tangent line at the point
*P*(*x*_{0},*y*_{0}) is

or equivalently

Knowing that

the equation of the tangent line becomes

**
**

**
[Back]
[Next]
**** **
[Trigonometry]
[Calculus]
[Geometry]
[Algebra]
[Differential Equations]
[Complex Variables]
[Matrix Algebra]

S.O.S MATHematics home page
Do you need more help? Please post your question on our
S.O.S. Mathematics CyberBoard.

*Mohamed A. Khamsi
*

Copyright © 1999-2017 MathMedics, LLC. All rights reserved.

Contact us

Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA

users online during the last hour