Implicit+Differentiation

= Implicit Differentiation is used when you have a relation, not a function. =
 * **For example: [[image:CodeCogsEqn_(15).gif]]**

Steps to solving implicit differentiation

 * 1) Derive everything, but chain rule everything as well - REMINDER: anything could be "chain ruled"
 * 2) Solve for dy/dx

**Example:**
find of

*derive everything

[[image:CodeCogsEqn(1).gif]]
note that the derivative of x is dx/dx which cancels to equal 1 so the derivative can be written as:

*get all dy/dx on the same side

*factor out the dy/dx

*solve for dy/dx

Tangent lines
Once you get a faction for the derivative, that can be used to find the slope at a particular point on the graph. To do this plug the x and y values into the derivative.


 * Things to remember:**
 * 1) If the denominator of the derivative comes out to equal zero, the tangent line is vertical at that point, and therefore the slope is undefined.
 * 2) If the numerator of the derivative comes out to equal zero, the tangent line is horizontal at that point, and therefore the slope is 0.
 * 3) To find the slope of the tangent line when the graph crosses the x-axis, plug the point when y=0 into the derivative.

Practice Question
find of

answer: