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

Lösung

ableitung von

(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

\int \frac{2}{4 - 9 x ^{2}} d x

x \to - 4 lim (6 - 3 x)

d er i v a t i v e y = x^{2} 2^{x^{2}}

(x + 3 t) \frac{d x}{d t} + 3 x - t = 0

\frac{d y}{d x} + \frac{7 y}{x} = - 5 x - 10