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Beliebt Rechnen >

derivative x(x^2+4)^5

Lösung

ableitung von

x (x^{2} + 4)^{5}

Lösung

(x^{2} + 4)^{5} + 10 x^{2} (x^{2} + 4)^{4}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = (x^{2} + 4)^{5}

= \frac{d x}{d x} (x^{2} + 4)^{5} + \frac{d}{d x} ((x^{2} + 4)^{5}) x

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

\frac{d}{d x} ((x^{2} + 4)^{5}) = 10 x (x^{2} + 4)^{4}

= 1 \cdot (x^{2} + 4)^{5} + 10 x (x^{2} + 4)^{4} x

Vereinfache

1 \cdot (x^{2} + 4)^{5} + 10 x (x^{2} + 4)^{4} x : (x^{2} + 4)^{5} + 10 x^{2} (x^{2} + 4)^{4}

= (x^{2} + 4)^{5} + 10 x^{2} (x^{2} + 4)^{4}

Graph

Beliebte Beispiele

derivative f(x)=5x+2x^2+7e^x

d er i v a t i v e f (x) = 5 x + 2 x^{2} + 7 e^{x}

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a re a y = - x^{2} + 1, y = 0

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\int_{0}^{π} \frac{1}{π - x} d x

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x \to - \frac{5}{2} lim (- x + 2)

derivative of cos(x-1)

\frac{d}{d x} (cos (x) - 1)