Page 330 - DMTH201_Basic Mathematics-1

Unit 12: Successive Differentiation

12.3 Summary Notes

It is extension of differentiation of one variable function successive.
Consider,

A one variable function,
y = f(x) (x is independent variable and y depends on x.)
Here if we make any change in x there will be a related change in y.
(n)
th
f (x) denotes n derivative of f.
th
Value of n derivative of y = f(x) at x = a is denoted by,
n
d y
n
f (a), y (a), or
n n
dx
x a
n
(i.e. value can be obtained by just replacing x with a in f (x).)
12.4 Keyword
Successive Differentiation: If y = f(x) is a differentiable function then by differentiating it w.r.t. x,
dy
we get f x
dx

12.5 Self Assessment

-1
1. y e a sin x (1 x 2 )y (2n 1)xy is equal to:
n 2 n 1
2
2
2
2
(a) (n + n )y (b) (n a )y
n n
(b) (n + a )y (d) (n a )y
2
2
2
2
n n
2
d y dy
2. x cos ,y sin5 1 x 2 x is equal to:
dx 2 dx
(a) 5y (b) 5y
(c) 25y (d) 25y
2
d y
1
3. y sin x 1 x 2 is equal to:
dx 2
dy
(a) x (b) 0
dx
dy dy 2
(c) x (d) x
dx dx
th
4. If y is the k derivative of y with respect to x, y = cos(sin x) then y sin x + y cos x is equal to:
k 1 2
3
3
(a) y sin x (b) y sin x
(c) y cos x (d) y cos x
3
3
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