Back to: Further Mathematics SS2
Find the derivative of each of the following:
HIGHER DERIVATIVES OF THE SECOND AND THIRD ORDER . DIFFERENTIATION OF IMPLICIT FUNCTIONS
Find the second and third derivatives of (1) cos 6x ( 2) 4x5 -5x
So far, we have treated relations. Of the form y = f (x). Examples of such relations are y = 3x2 – 2x + 1, y = 1 +
In any of these relations, y is said to be expressed explicitly in terms of x. The derivative of y with respect to x can be found from the rules of differentiation which have been discussed in the previous units.
Sometimes, the relationship between y and x may not be expressed explicitly.
For example, consider x2y + xy3 + 3x = 0. Here, the relation between y and x is not expressed explicitly. The relationship between y and x is said to be implicit.
In differentiating x2y+xy3+3x=0, y is treated as if it is a function of x and the rules of differentiation are applied in the appropriate manner. The process of differentiating implicit function is called implicit differentiation.
Differentiate the followings ;
(i) y= (3x+4) (6x-8)
(ii) y = 6x+7/2x-3
1) Differentiate y = ( 7x4 – 6 )5
2) Differentiate y = ( 2x + 5) ( 6x – 8)
3) Find the derivative of y = 3x2 – 5/x + 3
4) Find the derivative of y = 8/ ( 9 – x5)4
5) Find the derivative of y = 2x4 -5x3 -+ 6
6) If x3– y2 + 6xy = 0 find dy/dx
7) Find d3y/dx3 given that y = 8x5 – 3x4 + 9x3 -7x2 +6x+4
New Further MathsProject 2 page 121 – 126
1) If y = 3x4 -7x + 5 find dy/dx a) 12x3 b) 12x3 – 7 c) 12x3 + 5 d) 12x3 + 12
2) Find the second derivative of cos 5x a) 5sin5x b) -25cos5x c) 25cos5x d) -25sin5x
3) 2) If x2y + 4xy =1 find dy/dx a) 4+2xy/x2 b) 4-2xy/x2 c) -4-2xy/x2 d) -4+2xy/x
4) Given that y = x2 + 3x + 2, find dy/dx at x = 2 a) 6 b) 4 c) 7 d) 5
5) Given that y = ( 2x + 3)4 find dy/dx a) 18(2x + 3)3 b) 4(2x + 3)4 c) 8(2x + 3)3 d) 2( 2x+3)3
1) Differentiate y = (2x2 -3)3/x
2) Differentiate y = (2x+ 3)3 (4x2 -1)2How Can We Make ClassNotesNG Better - CLICK to Tell Us💃
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