2. Implicit & Explicit Forms
Implicit Form Explicit Form Derivative
Explicit: y in terms of x
Implicit: y and x together
Differentiating: want to be able to use either
1
xy 1
1
x
x
y 2
2 1
x
x
dx
dy
3. Differentiating with respect to x
Derivative →
Deriving when denominator agrees → use properties
Deriving when denominator disagrees → use chain rule & properties
dx
d
2
4x
dx
d
x
8 Denominator agrees -
properties
2
3y
dx
d
dx
dy
y
6 Denominator disagrees –
chain rule
