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Beliebt Rechnen >

derivative of x^2ln(5x)

Lösung

\frac{d}{d x} (x^{2} ln (5 x))

Lösung

2 x ln (5 x) + x

Schritte zur Lösung

\frac{d}{d x} (x^{2} ln (5 x))

Wende die Produktregel an:

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

f = x^{2}, g = ln (5 x)

= \frac{d}{d x} (x^{2}) ln (5 x) + \frac{d}{d x} (ln (5 x)) x^{2}

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

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

= 2 x ln (5 x) + \frac{1}{x} x^{2}

\frac{1}{x} x^{2} = x

= 2 x ln (5 x) + x

Graph

Beliebte Beispiele

derivative (x-2)^2

d er i v a t i v e (x - 2)^{2}

faktorisieren 7p^3+4p

f a c t or 7 p^{3} + 4 p

derivative 2e^{3x}

d er i v a t i v e 2 e^{3 x}

integral of ((sqrt(x)-2)^2)/x

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

(\partial)/(\partial x)(5^{2x})

\frac{\partial}{\partial x} (5^{2 x})