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Beliebt Rechnen >

derivative f(x)=x^2e^{6x}

Lösung

ableitung von

f (x) = x^{2} e^{6 x}

Lösung

2 x e^{6 x} + e^{6 x} \cdot 6 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = e^{6 x}

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

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

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

= 2 x e^{6 x} + e^{6 x} \cdot 6 x^{2}

Graph

Beliebte Beispiele

derivative of cos(x-4tan(x))

\frac{d}{d x} (cos (x) - 4 tan (x))

derivative of xarctan(x)

\frac{d}{d x} (x arctan (x))

2y^{''}-y^'+3y=0

2 y^{^{''}} - y^{^{'}} + 3 y = 0

x^2y^{''}-14xy^'+56y=0

x^{2} y^{^{''}} - 14 x y^{^{'}} + 56 y = 0

integral of ((x^3+2x^2-4)/(x^2))

\int (\frac{x ^{3} + 2 x ^{2} - 4}{x ^{2}}) d x