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Beliebt Rechnen >

derivative of x^2*e^{2x}

Lösung

\frac{d}{d x} (x^{2} \cdot e^{2 x})

Lösung

2 x e^{2 x} + e^{2 x} \cdot 2 x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{2} e^{2 x})

Wende die Produktregel an:

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

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

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

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

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

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

Graph

Beliebte Beispiele

integral of (2^{2x})/(1+2^{2x)}

\int \frac{2 ^{2 x}}{1 + 2 ^{2 x}} d x

xy^2y^'=y^3-5x^3,y(1)=2

x y^{2} y^{^{'}} = y^{3} - 5 x^{3}, y (1) = 2

tangent f(x)=-x^2+4

t an g e n t f (x) = - x^{2} + 4

derivative sin(x)+4/5 cot(x)

d er i v a t i v e sin (x) + \frac{4}{5} cot (x)

tangent f(x)=3x^2-4x+1,\at x=2

t an g e n t f (x) = 3 x^{2} - 4 x + 1, at x = 2