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Beliebt Rechnen >

derivative of x^6e^{2.5x}

Lösung

\frac{d}{d x} (x^{6} e^{2.5 x})

Lösung

6 x^{5} e^{2.5 x} + e^{2.5 x} \cdot 2.5 x^{6}

Schritte zur Lösung

\frac{d}{d x} (x^{6} e^{2.5 x})

Wende die Produktregel an:

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

f = x^{6}, g = e^{2.5 x}

= \frac{d}{d x} (x^{6}) e^{2.5 x} + \frac{d}{d x} (e^{2.5 x}) x^{6}

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

\frac{d}{d x} (e^{2.5 x}) = e^{2.5 x} \cdot 2.5

= 6 x^{5} e^{2.5 x} + e^{2.5 x} \cdot 2.5 x^{6}

Graph

Beliebte Beispiele

derivative of e^{-0.02x}

\frac{d}{d x} (e^{- 0.02 x})

integral of (e^x)/(2x)

\int \frac{e ^{x}}{2 x} d x

y^{''}+2y^'+4y=5sin(t)

y^{^{''}} + 2 y^{^{'}} + 4 y = 5 sin (t)

integral of (-x^2-3x+6)^2

\int (- x^{2} - 3 x + 6)^{2} d x

y^{''}-5y^'+6y=0,y(0)=0,y^'(0)=0

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 0, y^{^{'}} (0) = 0