Jawapan:
(2x) ^ 3 * 3 ^ (2x))) = warna (merah) (1 / (2sqrt (2))) * x ^ (warna (merah) (-3/2)) * warna (merah) ((sqrt (2) / 3)) ^ x #
Penjelasan:
#sqrt ((x ^ 2 * 2 ^ x) / ((2x) ^ 3 * 3 ^ (2x))) #
#color (putih) ("XXX") = warna (biru) (sqrt (x ^ 2) / (sqrt ((2x) ^ 3) (2x))) #
Mengambil komponen-komponen ini satu-satu masa (dan andaian #x> 0 #)
```````````````````````````````````````````
#color (biru) (sqrt (x ^ 2)) = warna (coklat) x #
#color (biru) (1 / sqrt ((2x) ^ 3)) = 1 / ((2x) ^ 3) ^ (1/2) = 1 / ((2x) ^ (3/2) (2 ^ (3/2) * x ^ (3/2)) = 1 / (2sqrt (2) * x ^ (3/2)) = warna (coklat) (1 / (2sqrt (2) (-3/2)) #
warna merah (warna) ("XXX") warna (biru) (sqrt (x ^ 2) / (sqrt ((2x) ^ 3 * 3 ^ (2x) (1 / (2sqrt (2)) x ^ (- 3/2)) = warna (merah) (1 / (2sqrt (2)) * x ^ (- 1/2)
~~~~~~~~~~~~~~~~~~~~~~~~~
#color (hijau) (sqrt (2 ^ x)) = warna (coklat) (sqrt (2) ^ (x)) #
#color (hijau) (1 / sqrt (3 ^ (2x))) = 1 / (3 ^ x) = warna (coklat) ((1/3) ^ x)
warna merah (putih) ("XXX") (hijau) (sqrt (2 ^ x) / sqrt (3 ^ (2x))) = warna (merah) ((sqrt (2) / 3) ^ x)
