AP Calc. Implicit Differentiation

implicit

some function of x and y = something else

• like circle equation

circle equation

(x-h) + (y-k) = rs

step to solve circle equation

plug in point and radius

step one of id

show derivative notation on both sides of the equal sign

• d/dx

step two of id

derive both sides of the equation with respect to x by using rules and dx/dx (=1) or dy/dx

step three of id

clean up (dx/dx=1)

number d is

always zero

step four of id

move all dy/dx to one side

step five of id

get dy/dx by itself

dy/dx

slope

dx/dx

1

find y when x = number

plug in x to circle equation

square root answers always have

plus or minus

• must find slope (dy/dx) of both

goal

dy/dx by itself

if given a point

plug in at the end of id

taking second d implicitly

derive twice

• plug in first derivative for any dy/dx though

chain rule

shell derivative (chocolate original) times chocolate derivative

product rule

f’*g+g’*f

quotient rule

f’*g-g’*f/gs

power rule

move original to front then subtract one from power

e to the x

e to the x

ln x

1/x

a to the x

a to the x times ln a