Implicit+Differentiation

=__Implicit Differentiation__=

You will occasionally find equations that are very difficult to find the derivative of traditionally. That is, solve for y and then take the derivative. Many times when this occurs, it is easier to take the derivative without solving for one variable, called implicit differentiation. In implicit differentiation, you will take the derivative of every variable with respect to one variable.

Take a look at the following examples.

Find the derivative of: 2x+3y=5 using implicit differentiation.
 * Example One **

Solution:

Find the derivative of y 2 +x 2 =1 implicitly.
 * Example Two **

Solution:

Write an equation to the tangent line of y 2 =3x+7, when at the point (-1,2).
 * Example Three **

Solution: