implicit -phoebe
TRANSCRIPT
IMPLICITSolve this or I will eat you!
5498 yxFind dy/dx of this equation:
5498 yx
Find dy/dx of this equation:
Shrek! Help me! Do you know how to solve for this? It is different from all problems I
have ever learned.
5498 yxDon’t worry! It called implicit differentiation. This is how you solve
for it.
8
7
98
78 89
yx
dxdy
dxdx
dxdy xy
REMEMBER: every time you differentiate implicitly an equation, differentiate the equation normally but always write d */dx next to whichever you take the differentiation of and separate d */dx by itself.
3)( 2532 yxyx
How about this one? Orge!
Find y’:
There’s no way he can know it while I can’t!
vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
vvvvvvvvvvvvvvvvf
Just use chain rule and product rule correctly and then separate y’
by itself.
yyxyx
yxxyy
yxxyyyyyxyx
yyxyyxyyxyx
yyxyyyxyx
yyyxyx
2)(15
)(101'
)(101'2')(15
'21)2()(5)'3()(5
'21)2)'3(()(5
'21)'()(5
43222
4323
432343222
343222432
322432
32432
5498 yx
Oh baby! Why you look so sad?
Meoww meow meowww meeow meww! ( I don’t know how to do my
homework!)
Don’t worry.I’m always at your service!
Meow meoww ( do this trig question)
yx 2sin212cos
y
xy
yyx
yyyx
yx
2sin
2sin'
2sin'22sin2
cossin'42sin2
sin212cos 2
You know, you do the same for trig problems but
careful with the simplification.
yyx 9sincos3
Hey! I come up with this question. It’s your turn to do it Dragon.
y
xy
xyyy
yyyxx
yyx
cos9
cos3'
cos3cos''9
'9cos'sincos2
9sincos
2
2
2
3
yyx 9sincos3
Careful with your chain and product rule and you will be just fine!
xyxy 22
Find the tangent line of the equation at x=1
Now it’s your turn! Try this one!
2)1(223
6
12.1.2
22)1(',2
1)1(113
3
1)1.(1.2
)1(2)1(',1
212
1
12
2'
2''.2
2
2
1
2
2
2
2
xyymy
xyymy
yyyy
x
xy
yy
yyyxy
Equation of the first tangent line.
Equation of the second tangent line.In this example, at x=1 we have 2 y-value
so we also have 2 equations of the tangent line.
Plug both x and y in the derivative equation to find m.