Svar:
(2x) ^ 3 * 3 ^ (2x))) = farve (rød) (1 / (2sqrt (2))) * x ^ (farve (rød) (-3/2)) * farve (rød) ((sqrt (2) / 3)) ^ x #
Forklaring:
#sqrt ((x ^ 2 * 2 ^ x) / ((2x) ^ 3 * 3 ^ (2x)))
#color (hvid) ("XXX") = farve (blå) (sqrt (x ^ 2) / (sqrt ((2x) ^ 3)) * farve (grøn) (sqrt (2 ^ x) / sqrt (2x))) #
Tager disse komponenter one-at-a-time (og antager #x> 0 #)
```````````````````````````````````````````
#COLOR (blå) (sqrt (x ^ 2)) = farve (brun) x #
#COLOR (blå) (1 / sqrt ((2x) ^ 3)) = 1 / ((2x) ^ 3) ^ (1/2) = 1 / ((2x) ^ (3/2)) = 1 / (2/2) * x ^ (3/2)) = farve (brun) (1 / (2sqrt (2)) x ^ (-3/2)) #
#rarr farve (hvid) ("XXX") farve (blå) (sqrt (x ^ 2) / (sqrt ((2x) ^ 3 * 3 ^ (2x)))) = Farve (brun) x * Farve) (1 / (2sqrt (2)) x ^ (- 3/2)) = farve (rød) (1 / (2sqrt (2)) * x ^
~~~~~~~~~~~~~~~~~~~~~~~~~
#COLOR (grøn) (sqrt (2 ^ x)) = farve (brun) (sqrt (2) ^ (x)) #
#COLOR (grøn) (1 / sqrt (3 ^ (2x))) = 1 / (3 ^ x) = farve (brun) ((1/3) ^ x) #
#rarr farve (hvid) ("XXX") farve (grøn) (sqrt (2 ^ x) / sqrt (3 ^ (2x))) = farve (rød) ((sqrt (2) / 3) ^ x)
