Paper 4: Fundamentals of Business Mathematics & Statistic

3.24 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Calculus

Now dxdy=δ →limx 0 δδxy=δ →limx 0f x x f x( + δδx)− ( )=h 0lim→f(x h) f x+h−( ), provided this limit exists.

Note : dydx does not mean the product of dxdwith y. The notation dxdstands as a symbol to denote the

operation of differentiation only. Read dydx as ‘dee y by dee x’.

SUMMARY :

The whole process for calculating f′ (x) or dydx may be summed up in the following stages :

1. Let the independent variable x has an increment h and then find the new value of the function
   f (x + h).


2. Find f(x + h) – f(x).


3. Divide the above value by h i.e., find ( )
   f(x h) f x.
   h

+ −

4. Calculate limh→ 0 f x h f(x)( +h)− =f (x)′

SOME USEFUL DERIVATIVES :

1. dxdx nxn= n 1− 2. dxd 1.x xn= − nn 1+.


2. dxde e .x= x 4. dxda a log a.x= x e


3. dxdlog x .e =^1 x 6. dxd(log x log e.a )=^1 x a


4. ddxc=^0 (c = constant)


5. dxd (u v)± =du dvdx dx±


6. dxd(uv) u v= dv dudx dx+

10. 2

du dvu

d u vdx dx

dx v v

−

=

11. dy dy dudx du dx= ⋅