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Beliebt Rechnen >

derivative of 7x^2ln(x)

Lösung

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

Lösung

7 (2 x ln (x) + x)

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

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

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

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

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

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

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

= 7 (2 x ln (x) + x)

Graph

Beliebte Beispiele

f(x)=-arctan(x)

f (x) = - arctan (x)

vereinfachen x5^{2x}

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derivative of 1/(sqrt(1-sin^2(x)))

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derivative (2t-1)(5t-5)^{-1}

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limit as x approaches 2 of 1/((x-2)^3)

x \to 2 lim (\frac{1}{( x - 2 ) ^{3}})