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(Select this problem) {

(Yes)

(No) } No.

f (x) = e ^2x

^{− 3x}

Let f (x) = e ^2x

^{− 3x} .

1.

f ⁽ⁿ⁾ (x)

^d

_dx ^f(x)

Show the following equality, where f ⁽ⁿ⁾ (x) represents ^d

_dx ^{f (x)}

.

f ⁽ⁿ⁺¹⁾ (x) − (4x − 3)f ⁽ⁿ⁾ (x) − 4nf ^{(n − 1)} (x) = 0 (n = 1, 2, . . .) 2. F _n (x) = f ⁽ⁿ⁾ (x)/f (x)

Let F n (x) = f ⁽ⁿ⁾ (x)/f (x). Show the following equality.

F _n ⁰ (x) = 4nF _{n − 1} (x) (n = 1, 2, . . .) 3.

Show the following equality.

F _n ⁰⁰ (x) + (4x − 3)F _n ⁰ (x) − 4nF _n (x) = 0 (n = 1, 2, . . .)