Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.37

Solution: Y = x log x
D.w.r. to x

dy

dx = x ×

1

x + log x.1
dy
dx = 1 + log x
D.w.r. to x

2

2

d y

dx = 0 +

1

x

= x^1

Example 80 :

If y = ax^2 + bx + C find

2
2
d y
dx
Solution: y = ax^2 + bx + C
D.w.r. to x

dy
dx = 2ax + b
D.w.r. to x
2
2
d y
dx = 2a
Example 81 :

If y = x^2 ex, Prove

2

2

d y

dx = (x

(^2) + 4x + 2)ex
Solution:
y = x^2 ex
D.w.r. to x
dy
dx= x
(^2) .ex + e (^2) .2x
= (x^2 + 2x)ex
D.w.r. to x
2
2
d y
dx = (x
(^2) + 2x) ex + ex (2x + 2)
= (x^2 + 2x + 2x + 2)ex
= (x^2 + 4x +2)ex