Page 82 - DECO403_MATHEMATICS_FOR_ECONOMISTS_ENGLISH

Unit 3: Differentiation

3.12 Summary Note

y G
z lim is known as Derivative for the differential coefficient of y function with respect to x.
x Go 0 xG
To avoid any doubt with respect to independent variables, the differential coefficient or
y d dy
y
derivative lim with respect to x is written as () or . This way the process of

0 x dx dx
xo
knowing the limit is known as differentiation or in other words method of calculating the
differential coefficient of any product is referred as Differentiation.
z If f(x) is the function of x and the same function of x + δx is f(x + δx), then limiting value is
x
( f x G ) x f ( )
lim , for the differential coefficient f(x) with respect to x.
x Go 0 x G
d d d
x
x
f
x
z { ( )} f 1 () r f 2 ()
dx dx dx
z Differential coefficient of Constant and multiplication of any product is equal to differential
coefficient of product and multiplication of constant value.
d x x
e
z () e
dx
d x x
z a a log a i.e. differential coefficient of division of two function
e
dx
3.13 Keywords
z Differential coefficient: Differentiation
z Growth: Increment

3.14 Review Questions

d 2

1. Find the value of (6x ) [Ans.: = –12x]
dx
d 6
x
2. Find the value of (5x 2 ) [Ans.: = 30x + 2]
5
dx
d x x
3. Prove that a a log a
e
dx
1
6 1
4. Find the differential coefficient of 6log x x 7 [Ans.: = x 2 ]
x 2
x dy

5. If y , then prove that x y (1 y )
x 5 dx
Answers: Self Assessment
1. (i) Differentiation (ii) Multiplication (iii) a (iv) n – 1 (v) 63x 6
2. (i) a (ii) (b) (iii) (c) (iv) (d) (v) (a)

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