derivative (1+6x^2)(x-x^2)

Lösung

ableitung von

(1 + 6 x^{2}) (x - x^{2})

- 24 x^{3} + 18 x^{2} - 2 x + 1

Schritte zur Lösung

\frac{d}{d x} ((1 + 6 x^{2}) (x - x^{2}))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 + 6 x^{2}, g = x - x^{2}

= \frac{d}{d x} (1 + 6 x^{2}) (x - x^{2}) + \frac{d}{d x} (x - x^{2}) (1 + 6 x^{2})

\frac{d}{d x} (1 + 6 x^{2}) = 12 x

\frac{d}{d x} (x - x^{2}) = 1 - 2 x

= 12 x (x - x^{2}) + (1 - 2 x) (1 + 6 x^{2})

Vereinfache

12 x (x - x^{2}) + (1 - 2 x) (1 + 6 x^{2}) : - 24 x^{3} + 18 x^{2} - 2 x + 1

= - 24 x^{3} + 18 x^{2} - 2 x + 1

x \to \infty lim (- 3 x^{2})

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (0) = b, y^{^{'}} (0) = 2

\frac{\partial}{\partial x} (cos (2 (2 y x - 1)))

\frac{\partial}{\partial x} (e^{x yz - 2})

x \to 0 + lim (\frac{2}{x ^{\frac{1}{3}}})