Найдите частные производные первого разряда: z=xy⁴+x³y³+sin y

f(х)\' = (4 * (х – 5)^(1 / 2))’ = 4 * (х – 5)’ *((х – 5)^(1 / 2))’ = 4 * ((х)’ – (5)’) *((х – 5)^(1 / 2))’ = 4 * (1 – 0) * (1 / 2) * (х – 5)^(-1 / 2) = 2 / √(х – 5).

f(х)\' = (х – 1)’ = (х)’ – (1)’ = (1 * х^0) – 0 = 1 * 1 – 0 = 1 – 0 = 1.

f(х)\' = ((-1 / 5) *х^3 + 45х^2 + 4х – 1)’ = ((-1 / 5) * х^3)’ + (45х^2)’ + (4х)’ – (1)’ =

(-1 / 5) * 3 * х^2 + 45 * 2 * х + 4 – 0 = (-3 / 5) * х^2 + 90х + 4.

f(х)\' = (4х^2 + 6х + 3)’ = (4х^2)’ + (6х)’ + (3)’ = 8х + 6 + 0 = 8х + 6.

f(х)\' = (1 – 6 * х^(1 / 3))’ = (1)’ – (6 * х^(1 / 3))’ = 0 – 6 * (1 / 3) * х^((1 / 3) – 1) = 2 * х^(2 / 3).