Найдите производную функции: y=4x√x-24x+38

интерпретируем 4x√x - 24x + 38 =                          [latex] = 4x \sqrt{x} - 24x + 38 \ ; [/latex] [latex] y'_x = ( 4x \sqrt{x} - 24x + 38 )'_x = ( 4x \cdot x^{1/2} )'_x - ( 24x )'_x + (38)'_x \ = \\\\ = 4 ( x^{1+0.5} )'_x - 24(x)'_x = 4 ( x^{1.5} )'_x - 24 = 4 \cdot 1.5 \cdot x^{1.5-1} - 24 = \\\\ = 6 x^{0.5} - 24 = 6 \sqrt{x} - 24 \ . [/latex]