implicit -phoebe

12
IMPLICIT Solve this or I will eat you! 54 9 8 y x Find dy/dx of this equation:

Upload: lucky0102

Post on 23-Jun-2015

509 views

Category:

Documents


1 download

TRANSCRIPT

Page 1: Implicit -phoebe

IMPLICITSolve this or I will eat you!

5498 yxFind dy/dx of this equation:

Page 2: Implicit -phoebe

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.

Page 3: Implicit -phoebe

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.

Page 4: Implicit -phoebe

3)( 2532 yxyx

How about this one? Orge!

Find y’:

There’s no way he can know it while I can’t!

Page 5: Implicit -phoebe

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

Page 6: Implicit -phoebe

Oh baby! Why you look so sad?

Meoww meow meowww meeow meww! ( I don’t know how to do my

homework!)

Page 7: Implicit -phoebe

Don’t worry.I’m always at your service!

Meow meoww ( do this trig question)

yx 2sin212cos

Page 8: Implicit -phoebe

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.

Page 9: Implicit -phoebe

yyx 9sincos3

Hey! I come up with this question. It’s your turn to do it Dragon.

Page 10: Implicit -phoebe

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!

Page 11: Implicit -phoebe

xyxy 22

Find the tangent line of the equation at x=1

Now it’s your turn! Try this one!

Page 12: Implicit -phoebe

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.