Question

Вычислить производную

Answer 1

(xⁿ)' = nxⁿ⁻¹; ( x⁷' = 7x⁶; x⁰' = 0)
(a·f(x))' = a·f(x)'; ( 5x⁷' = 35x⁶; 5' = 0)
(f(x)+g(x))' = f(x)'+g(x)' ((5x⁷ + 5)' = 35x⁶ + 0)
(f(x)·g(x))' = f(x)'·g(x) + f(x)·g(x)'
(f(g(x)))' = f'(g(x))·g(x)' ((7·(4x³)⁶)' = 7·5(4x³)⁵·12x²)

y = (3x + 2)(6 - 2x)
y' = (3 + 0)(6 - 2x) + (3x + 2)(0 - 2) = 18 - 6x - 6x -4 = 12x + 14

y = 3x² + $sqrt[3]{xв}$ + 5$sqrt{x}$
y' = 6x  + $frac{2}{3 sqrt[3]{x} }$ + $frac{5}{2 sqrt{x} }$

y = (2x³ + 5)³
y' = 3(2x³ + 5)² · 6x² = 3(4x⁶ + 20x³ + 25)·6x² = 72x⁸ + 360x⁵ + 450x²