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Beliebt Rechnen >

derivative 10(4e^{x^2}x^3+6e^{x^2}x)

Lösung

ableitung von

10 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

Lösung

10 (8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}})

Schritte zur Lösung

\frac{d}{d x} (10 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 10 (\frac{d}{d x} (4 e^{x^{2}} x^{3}) + \frac{d}{d x} (6 e^{x^{2}} x))

\frac{d}{d x} (4 e^{x^{2}} x^{3}) = 4 (2 e^{x^{2}} x^{4} + 3 e^{x^{2}} x^{2})

\frac{d}{d x} (6 e^{x^{2}} x) = 6 (2 e^{x^{2}} x^{2} + e^{x^{2}})

= 10 (4 (2 e^{x^{2}} x^{4} + 3 e^{x^{2}} x^{2}) + 6 (2 e^{x^{2}} x^{2} + e^{x^{2}}))

Multipliziere aus

4 (2 e^{x^{2}} x^{4} + 3 e^{x^{2}} x^{2}) + 6 (2 e^{x^{2}} x^{2} + e^{x^{2}}) : 8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}}

= 10 (8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}})

Graph

Beliebte Beispiele

9y^{''}+30y^'+25y=0

9 y^{^{''}} + 30 y^{^{'}} + 25 y = 0

sum from n=0 to infinity of 3-7(0.6)^n

n = 0 \sum \infty 3 - 7 (0.6)^{n}

derivative 4/(\sqrt[3]{x)}

d er i v a t i v e \frac{4}{3 x}

fläche x+y^2=6,x+y=0

a re a x + y^{2} = 6, x + y = 0

derivative y=(x^6-7x+4)(x^4-5x)

d er i v a t i v e y = (x^{6} - 7 x + 4) (x^{4} - 5 x)