Question

Find the nth derivative of
(a)
y x x x  cos8 cos 4 co

Answer 1

Answer:

We have y=cos

4

x

Then y=

4

1

(2cos

2

x)

2

y=

4

1

(1+cos2x)

2

y=

4

1

(1+cos

2

2x+2cos2x)

y=

8

1

(1+cos4x)+

2

1

cos2x+

4

1

y

1

=

8

1

(−4sin4x)+

2

1

(−2sin2x)

y

1

=

8

1

(−4cos(

2

π

+4x))+

2

1

(2cos(

2

π

+2x))

y

2

=

8

1

(−16cos4x)+(

2

−1

)(4cos2x)

y

2

=

8

1

(−16cos4x+π)+(

2

1

)(2

2

cos(π+2x))

y

n

=2

n−1

cos(

2

nπ

+2x)+2

2n−3

cos(

2

nπ

+4x)