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Beliebt Rechnen >

derivative of (x+1(x^3+x-2))

Lösung

\frac{d}{d x} ((x + 1) (x^{3} + x - 2))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} ((x + 1) (x^{3} + x - 2))

Wende die Produktregel an:

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

f = x + 1, g = x^{3} + x - 2

= \frac{d}{d x} (x + 1) (x^{3} + x - 2) + \frac{d}{d x} (x^{3} + x - 2) (x + 1)

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

\frac{d}{d x} (x^{3} + x - 2) = 3 x^{2} + 1

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of 5/((x-1)(x^2+4))

\int \frac{5}{( x - 1 ) ( x ^{2} + 4 )} d x

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8x^7y+x^8y^'=-5sec^2(x)tan(x)

8 x^{7} y + x^{8} y^{^{'}} = - 5 sec^{2} (x) tan (x)

derivative of-x+y+2

\frac{d}{d x} (- x + y + 2)

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x \to \frac{π}{6} lim (\frac{sin ( x ) - sin ( \frac{π}{6} )}{x - \frac{π}{6}})