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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