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Beliebt Rechnen >

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

Lösung

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

Lösung

3 x^{2} - 2 x - 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (x + 1) = 1

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (e^{2x})/((1+e^{2x))^2}

\int \frac{e ^{2 x}}{( 1 + e ^{2 x} ) ^{2}} d x

t a y l or \frac{1}{x}

integral of (4sqrt(x)-1/(2sqrt(x)))

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

integral of 1/(y^2-16)

\int \frac{1}{y ^{2} - 16} d y

y^{^{'}} = t^{\frac{1}{4}} - y