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Beliebt Rechnen >

derivative x^4(2x-5)^6

Lösung

ableitung von

x^{4} (2 x - 5)^{6}

Lösung

4 x^{3} (2 x - 5)^{6} + 12 (2 x - 5)^{5} x^{4}

Schritte zur Lösung

\frac{d}{d x} (x^{4} (2 x - 5)^{6})

Wende die Produktregel an:

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

f = x^{4}, g = (2 x - 5)^{6}

= \frac{d}{d x} (x^{4}) (2 x - 5)^{6} + \frac{d}{d x} ((2 x - 5)^{6}) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} ((2 x - 5)^{6}) = 12 (2 x - 5)^{5}

= 4 x^{3} (2 x - 5)^{6} + 12 (2 x - 5)^{5} x^{4}

Graph

Beliebte Beispiele

y^{''}+40y^'+625y=0

y^{^{''}} + 40 y^{^{'}} + 625 y = 0

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\int_{0}^{1} \frac{17}{x ^{5}} d x

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\int x sin (- 2 x) d x