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Beliebt Rechnen >

derivative of (4x^{5x})

Lösung

\frac{d}{d x} ((4 x)^{5 x})

Lösung

5 ln (2) \cdot 2^{10 x + 1} x^{5 x} + 5 x^{5 x} (ln (x) + 1) \cdot 102 4^{x}

Schritte zur Lösung

\frac{d}{d x} ((4 x)^{5 x})

Vereinfache

(4 x)^{5 x} : 102 4^{x} x^{5 x}

= \frac{d}{d x} (102 4^{x} x^{5 x})

Wende die Produktregel an:

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

f = 102 4^{x}, g = x^{5 x}

= \frac{d}{d x} (102 4^{x}) x^{5 x} + \frac{d}{d x} (x^{5 x}) 102 4^{x}

\frac{d}{d x} (102 4^{x}) = 5 ln (2) \cdot 2^{10 x + 1}

\frac{d}{d x} (x^{5 x}) = 5 x^{5 x} (ln (x) + 1)

= 5 ln (2) \cdot 2^{10 x + 1} x^{5 x} + 5 x^{5 x} (ln (x) + 1) \cdot 102 4^{x}

Graph

Beliebte Beispiele

integral of (3x)^2+sqrt(2)

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

limit as x approaches 1 of 1-sqrt(2-x)

x \to 1 lim (1 - 2 - x)

derivative of arccos(x^3)

\frac{d}{d x} (arccos (x^{3}))

derivative of 2*x^2

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

inverselaplace ((s-2))/((s-3)(s+1))

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