Ch 16 - implicit differentiation

what r the steps to implicit differentiation

1. Take derivative off both sides

2. put all y’ terms to one side of equation

3. factor out y’

4. solve for y’

when taking the derivative of d/dx(y) ALWAYS mult by ___.

y’

when finding derivatives always rewrite radicals as ____ to make the process easier

powers

how to explicitly differentiate

1. solve for y

2. differentiate (take derivative) as usual

what is an explicit function

you can solve for y

what is an implicit function

the y’s and x’s are mixed together so well that you cant solve for y

how to solve differentiation “?” when given coordinates

1. d/dx both sides

2. Substitute coordinates

3. solve for y’ and wtv else question wants

For vertical tangent line, what does y’ =?

denominator equals 0 (undefined)

For vertical horizontal line, what does y’ =?

0

How to find the (x,y) points where a curve has vertical and horizontal tangent lines

1. find y’

2. find horizontal tangent line points

   1. y’ = 0

   2. find zeroes to get x value

   3. plug in x values to find y

   4. done answer is (x,y)

3. Find vertical tanget line points

   1. y’ = undefined

   2. find zeroes to get x value

   3. plug in x values to find y

   4. done answer is (x,y)