Question

Find the nth derivative of x^4 /(x-1) (1-2)
$x {}^{4 \div (x - 1)(x - 2)}$
​

Answer 1

Answer:

y=

(x−a)(x+a)

1

=

2a

1

(

x−a

1

−

x+a

1

)

dx

dy

=

2a

1

(

(x−a)

2

−1

−(−

(x+a)

2

1

))

dx

2

d

2

y

=

2a

1

(

(x−a)

3

2!

−(

(x+a)

3

2!

))

dx

3

d

3

y

=

2a

−1

(

(x−a)

4

3!

−(

(x+a)

4

3!

))

Following the pattern we get

dx

n

d

n

y

=

2a

(−1)

n

n!(

(x−a)

n+1

1

−

(x+a)

n+1

1

)