Pitanje # 36b8c

Množenjem, Delta H (x) = (x-x sqrt {}) (x + sqrt {x}) = x ^ 2-x #

Po pravilu Power, Delta H "(x) = 2x-1 #.

Nadam se da je to bilo od pomoći.

Ako to primijetite Delta H (x) * je razlika savršenih kvadrata, onda je problem mnogo lakši.

Ako to ne učinite, možete koristiti Pravilo proizvoda.

Delta H '(x) = uv' + vu "#

Delta H (x) = uv = (x-sqrt (x)) (x + sqrt (x)) = (x-x ^ (1/2)), (x + x ^ (1/2)) *

Delta H "(x) = (xx ^ (1/2)) (1 + 1 / 2x ^ (- 1/2)) + (x + x ^ (1/2)) (1-1 / 2 x ^ (-1/2)) #

Delta H "(x) = (xx ^ (1/2)) (1 + 1 / (2 x ^ (1/2))) + (x + x ^ (1/2)) (1-1 / (2x ^ (1/2))) *

Delta H "(x) = x + x / (2 x ^ (1/2)) - ^ x (1/2) -X ^ (1/2) / (2 x ^ (1/2)) + xx / (2x ^ (1/2)) + x ^ (1/2) -X ^ (1/2) / (2 x ^ (1/2)) *

Delta H "(x) = x + x / (2 x ^ (1/2)) - ^ x (1/2) -1 / 2 + xx / (2 x ^ (1/2)) + x ^ (1 / 2) -1/2 #

Delta H "(x) = x + x / (2 x ^ (1/2)) - ^ x (1/2) + xx / (2 x ^ (1/2)) + x ^ (1/2) -1 #

Delta H "(x) = x + x / (2 x ^ (1/2)) + x-x / (2 x ^ (1/2)) - 1 #

Delta H "(x) = x + x-1 #

Delta H "(x) = 2x-1 #