IMPLICIT DIFFERENTIATION

BLAKE FARMAN

Lafayette College

Name:

Use implicit di↵erentiation to find dy/ dx.

1. 2x2 + xy � y2 = 2

2. x3 � xy2 + y3 = 1

Date: February 24, 2019.

1

Solutions

Caitxy y2 4x t Cgt xy 2gy O

4xty 2gy xy 2g x y

y If I T0 3 2

ly'tx2yyD t3gy3 2y 2xyy t3g y

y2 3 2 12xy t3g

2y

j gjz

2 IMPLICIT DIFFERENTIATION

3. y5 + x2y3 = 1 + x4y

4. cos(xy) = 1 + sin(y)

5. y sin(x2) = x sin(y2)

5y4y t 2xy3tX43yy'D Of 43y t x4y

5y4y t 32

yy t2xgs 4x3ytx4ySy4g t 3

2yy xly y Sy4 3 25 x

4 43y 2xg3

y fIEIEDsin Xy ytxy Ot cosg y cos g y

ysincxy xy'sinKycoslyly

ysincxy cosg y Xy'sinGg Koscy t xsinky yysin Xy

y cTxsinCxyT

daysin ysin t ycos14Ex y sin t 2xycos XY

Ix xsinly4 sing2 t x cos dodgy sin151 t 2xyyCody4

y sin t 2xycosXY sinks t 2xyyCody4

ysince 2xyyCody4 sinly9 2xgoos XY

y sink 2xycoslya sin151 2xgas44

i

IMPLICIT DIFFERENTIATION 3

6. xy =px2 + y2

7. x sin(y) + y sin(x) = 1

8. tan(x� y) =y

1 + x2

9. You are given that f(1) = 2 and f(x) + x2f(x)3 = 10. Find f 0(1).