IMPLICIT DIFFERENTIATION - MadAsMaths

Created by T. Madas

IMPLICIT DIFFERENTIATION

Created by T. Madas

Created by T. Madas

BASIC DIFFERENTIATION

Created by T. Madas

Created by T. Madas

Question 1 For each of the following implicit relationships, find an expression for dy , in terms of

dx x and y .

a) x2 + 2xy + 3y2 = 12

b) y3 + xy - x2 = 0 c) 2x3 + 5xy2 - 2 y4 = 10

d) x2 y + 4xy2 = 2 y

dy = - x + y , dx x + 3y

dy dx

=

2x - y 3y2 + x

,

dy dx

=

6x2 8y3

+ 5y2 - 10 xy

,

dy dx

=

2y(x + 2y)

2 - x2 - 8xy

Created by T. Madas

Created by T. Madas

Question 2 For each of the following implicit relationships, find an expression for dy , in terms of

dx x and y .

a) y3 - x2 y2 = x2 + 3x +1

b) 8 y2 + x2 y3 = 10 - x5

c) (3x - y)(2x + 3y) = 8

( ) d) y x3 + y3 = ( x +1)( x + 4)

dy dx

=

2xy2 + 2x + 3 3y2 - 2 yx2

,

dy 2xy3 + 5x4

dx

=

- 16

y

+

3x2

y2

,

dy = 12x + 7 y , dx 6 y - 7x

dy 2x + 5 - 3yx2

= dx

4y3 + x3

Created by T. Madas

Created by T. Madas

Question 3 For each of the following implicit relationships, find an expression for dy , in terms of

dx x and y .

a) y3 + 3y = x3

b) 9( y + 2)2 = 5 + 4( x - 2)2

c) e2x + e2 y = xy

d) y2 ( x + 2) = x2

dy dx

=

x2 y2 +1

,

dy dx

=

4(x - 2) 9( y + 2)

,

dy y - 2 e2x dx = 2e2 y - x

,

dy = 2x - y2 dx 2xy + 4 y

Created by T. Madas

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