derivative 4x(x^2-1)

Lösung

ableitung von

4 x (x^{2} - 1)

4 (3 x^{2} - 1)

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

4 (1 \cdot (x^{2} - 1) + 2 xx) : 4 (3 x^{2} - 1)

= 4 (3 x^{2} - 1)

\int \frac{1}{36 x ^{2} + 1} d x

\frac{d}{d x} (- 4 x y)

\frac{\partial}{\partial y} (\frac{y}{1 + x ^{2} + y ^{2}})

\frac{d}{d x} (c x^{- 4})

n = 1 \sum \infty 3 (5)^{- n}