derivative f(x)=x^2(1-4x)

Lösung

ableitung von

f (x) = x^{2} (1 - 4 x)

2 x - 12 x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{2} (1 - 4 x))

Wende die Produktregel an:

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

f = x^{2}, g = 1 - 4 x

= \frac{d}{d x} (x^{2}) (1 - 4 x) + \frac{d}{d x} (1 - 4 x) x^{2}

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

\frac{d}{d x} (1 - 4 x) = - 4

= 2 x (1 - 4 x) + (- 4) x^{2}

Vereinfache

2 x (1 - 4 x) + (- 4) x^{2} : 2 x - 12 x^{2}

= 2 x - 12 x^{2}

t an g e n t f (x) = x^{3} - 6 x^{2} - 34 x + 40, at x = - 3

\int_{0}^{7} x 49 - x^{2} d x

\int_{0}^{2} x (x^{2} - 1)^{3} d x

\frac{\partial}{\partial x} (x^{2} y + 4 x^{4} y)

n = 3 \sum \infty \frac{1}{n ( n + 1 )}