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Beliebt Rechnen >

derivative y=x^2ln(7x)

Lösung

ableitung von

y = x^{2} ln (7 x)

Lösung

2 x ln (7 x) + x

Schritte zur Lösung

\frac{d}{d x} (x^{2} ln (7 x))

Wende die Produktregel an:

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

f = x^{2}, g = ln (7 x)

= \frac{d}{d x} (x^{2}) ln (7 x) + \frac{d}{d x} (ln (7 x)) x^{2}

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

\frac{d}{d x} (ln (7 x)) = \frac{1}{x}

= 2 x ln (7 x) + \frac{1}{x} x^{2}

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

= 2 x ln (7 x) + x

Graph

Beliebte Beispiele

limit as a approaches infinity of a^2

a \to \infty lim (a^{2})

integral of t^2e^{4t}

\int t^{2} e^{4 t} d t

integral of 9xe^{6x}

\int 9 x e^{6 x} d x

(dy)/(dx)=4+e^{y-4x+5}

\frac{d y}{d x} = 4 + e^{y - 4 x + 5}

derivative of e^{5-2x}

\frac{d}{d x} (e^{5 - 2 x})