Differentiation Short Questions (Question 1 - 5)


Question 1:
Differentiate the expression 2x (4x2 + 2x – 5) with respect to x.

Solution:
2x (4x2 + 2x – 5) = 8x3 + 4x2 – 10x
d dx (8x3 + 4x2 – 10x)
= 24x + 8x –10 


Question 2:
Given that y= x 3 +2 x 2 +1 3x , find  dy dx .
Solution:
y= x 3 +2 x 2 +1 3x y= x 3 3x + 2 x 2 3x + 1 3x y= x 2 3 + 2x 3 + 1 3 x 1 dy dx = 2x 3 + 2 3 1 3 x 2 dy dx = 2x 3 + 2 3 1 3 x 2

Question 3:
Given that y= 3 5x+1 , find  dy dx
Solution:
y= 3 5x+1 =3 ( 5x+1 ) 1 2 dy dx = 1 2 .3 ( 5x+1 ) 3 2 ( 5 ) dy dx = 15 2 [ ( 5x+1 ) 3 ] 1 2 dy dx = 15 2 ( 5x+1 ) 3

Question 4:
Find ds dt for each of the following functions.
(a) s= ( t 3 t ) 2 (b) s= ( t+1 )( 35t ) t 2

Solution:
(a)
s= ( t 3 t ) 2 s=( t 3 t )( t 3 t ) s= t 2 6+ 9 t 2 s= t 2 6+9 t 2 ds dt =2t18 t 3 =2t 18 t 3
(b)
s= ( t+1 )( 35t ) t 2 s= 3t5 t 2 +35t t 2 = 5 t 2 2t+3 t 2 s=5 2 t + 3 t 2 =52 t 1 +3 t 2 ds dt =2 t 2 6 t 3 = 2 t 2 6 t 3


Question 5:
Given that  y= 3 5 u 5, where u = 4+ 1. Find dy dx in terms of x.

Solution:
y= 3 5 u 5 , u=4x+1 y= 3 5 ( 4x+1 ) 5 dy dx =5. 3 5 ( 4x+1 ) 4 .4 dy dx =12 ( 4x+1 ) 4