derivative of (1+9x^2(x-x^2))

Lösung

\frac{d}{d x} ((1 + 9 x^{2}) (x - x^{2}))

- 36 x^{3} + 27 x^{2} - 2 x + 1

Schritte zur Lösung

\frac{d}{d x} ((1 + 9 x^{2}) (x - x^{2}))

Wende die Produktregel an:

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

f = 1 + 9 x^{2}, g = x - x^{2}

= \frac{d}{d x} (1 + 9 x^{2}) (x - x^{2}) + \frac{d}{d x} (x - x^{2}) (1 + 9 x^{2})

\frac{d}{d x} (1 + 9 x^{2}) = 18 x

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

= 18 x (x - x^{2}) + (1 - 2 x) (1 + 9 x^{2})

Vereinfache

18 x (x - x^{2}) + (1 - 2 x) (1 + 9 x^{2}) : - 36 x^{3} + 27 x^{2} - 2 x + 1

= - 36 x^{3} + 27 x^{2} - 2 x + 1

\frac{d}{d x} (arctan (arcsin (x)))

\int 3 y^{5} y^{3} + 1 d y

x \to - 1 lim (x + 2 x^{4})

\frac{d}{d x} (a x e^{- x})

\frac{\partial}{\partial x} (ln (a x + b y))