Question

Find the nth derivative of the function =6 .

Answer 1

Answer:

f(x)=

1−x

2

1

=

(1−x)(1+x)

1

=

2

1

[

1−x

1

+

1+x

1

]

dx

n

d

n

f(x)

=

2

1

dx

n

d

n

(

1+x

1

)+

2

1

dx

n

d

n

(

1+x

1

)

=

2

1

(1−x)

n+1

(−1)

n

.n!(−1)

n

+

2

1

(1+x)

n+1

(−1)

n

.n!(1)

n

When n is even

=

2

1

(1−x)

n+1

n!

+

2

1

(1+x)

n+1

n!

∴ at x=0

dx

n

d

n

f(x)

=

2

1

.

1

n1

+

2

1

.

1

n!

=

2

1

.2n!

dx

n

d

n

f(o)

=n!

, when n is even .

Step-by-step explanation:

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