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Beliebt Rechnen >

derivative of xe^{x^6}

Lösung

\frac{d}{d x} (x e^{x^{6}})

Lösung

e^{x^{6}} + 6 e^{x^{6}} x^{6}

Schritte zur Lösung

\frac{d}{d x} (x e^{x^{6}})

Wende die Produktregel an:

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

f = x, g = e^{x^{6}}

= \frac{d x}{d x} e^{x^{6}} + \frac{d}{d x} (e^{x^{6}}) x

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

\frac{d}{d x} (e^{x^{6}}) = e^{x^{6}} \cdot 6 x^{5}

= 1 \cdot e^{x^{6}} + e^{x^{6}} \cdot 6 x^{5} x

Vereinfache

1 \cdot e^{x^{6}} + e^{x^{6}} \cdot 6 x^{5} x : e^{x^{6}} + 6 e^{x^{6}} x^{6}

= e^{x^{6}} + 6 e^{x^{6}} x^{6}

Graph

Beliebte Beispiele

derivative 2(12)(18)+2(9)

d er i v a t i v e 2 (12) (18) + 2 (9)

(dr)/(dθ)=8cos(θ)

\frac{d r}{d θ} = 8 cos (θ)

\int 92

limit as t approaches 0 of ((3^t-2^t))/t

t \to 0 lim (\frac{( 3 ^{t} - 2 ^{t} )}{t})

integral of ((3x-2))/(1-6x-9x^2)

\int \frac{( 3 x - 2 )}{1 - 6 x - 9 x ^{2}} d x