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Beliebt Rechnen >

derivative y=x^2ln(x^2)

Lösung

ableitung von

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

Lösung

2 x ln (x^{2}) + 2 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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

= 2 x ln (x^{2}) + 2 x

Graph

Beliebte Beispiele

derivative of sqrt(\sqrt{1+\sqrt{x)}+1}

derivative ln(sqrt(x+3))

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

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(dy)/(dx)=5+e^{y-5x+1},y(0)=-1