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Beliebt Rechnen >

derivative f(x)=x^3(x^4-1)

Lösung

ableitung von

f (x) = x^{3} (x^{4} - 1)

Lösung

7 x^{6} - 3 x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{3} (x^{4} - 1))

Wende die Produktregel an:

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

f = x^{3}, g = x^{4} - 1

= \frac{d}{d x} (x^{3}) (x^{4} - 1) + \frac{d}{d x} (x^{4} - 1) x^{3}

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

\frac{d}{d x} (x^{4} - 1) = 4 x^{3}

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

Vereinfache

3 x^{2} (x^{4} - 1) + 4 x^{3} x^{3} : 7 x^{6} - 3 x^{2}

= 7 x^{6} - 3 x^{2}

Graph

Beliebte Beispiele

derivative of (-x^2-4/((x^2-4)^2))

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

steigung (x^2+4)y=8

s l o p e (x^{2} + 4) y = 8

integral from 0.5 to 1.5 of (1/8+3/8 x)

\int_{0.5}^{1.5} (\frac{1}{8} + \frac{3}{8} x) d x

integral of (3csc^2(4x))

\int (3 csc^{2} (4 x)) d x

d/(dv)(v/(u-v))

\frac{d}{d v} (\frac{v}{u - v})