derivative of x(x-1^2)

Lösung

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

3 x^{2} - 4 x + 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= 3 x^{2} - 4 x + 1

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

in v erse l a pl a ce \frac{1}{3 s}

\frac{\partial}{\partial x} (x^{2} y z^{2})

\frac{\partial}{\partial y} (2 x ln (y) - yz)

s im pl i f y (e^{- x} - e^{5}) (e^{x} + e^{- 2})