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Beliebt Rechnen >

(xe^{x^2})^'

Lösung

(x e^{x^{2}})^{^{'}}

Lösung

e^{x^{2}} + 2 e^{x^{2}} x^{2}

Schritte zur Lösung

(x e^{x^{2}})^{'}

Wende die Produktregel an:

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

f = x, g = e^{x^{2}}

= x^{^{'}} e^{x^{2}} + (e^{x^{2}})^{^{'}} x

x^{'} = 1

(e^{x^{2}})^{'} = e^{x^{2}} \cdot 2 x

= 1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx

Vereinfache

1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx : e^{x^{2}} + 2 e^{x^{2}} x^{2}

= e^{x^{2}} + 2 e^{x^{2}} x^{2}

Graph

Beliebte Beispiele

(\partial)/(\partial x)(e^{xy-y})

\frac{\partial}{\partial x} (e^{x y - y})

derivative e^{3xcos(2x)}

d er i v a t i v e e^{3 x c o s (2 x)}

derivative y=-3/x+2/(x^3)

d er i v a t i v e y = - \frac{3}{x} + \frac{2}{x ^{3}}

integral of (7-x^2)/(3x^3+x)

\int \frac{7 - x ^{2}}{3 x ^{3} + x} d x

tangent f(x)=x^2+x,\at a=5

t an g e n t f (x) = x^{2} + x, at a = 5