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Beliebt Rechnen >

derivative of 4x^2ln(x)

Lösung

\frac{d}{d x} (4 x^{2} ln (x))

Lösung

4 (2 x ln (x) + x)

Schritte zur Lösung

\frac{d}{d x} (4 x^{2} ln (x))

Entferne die Konstante:

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

= 4 \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)

= 4 (\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}

= 4 (2 x ln (x) + \frac{1}{x} x^{2})

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

= 4 (2 x ln (x) + x)

Graph

Beliebte Beispiele

f (x) = x + 9

derivative of x/(1+sqrt(x))

\frac{d}{d x} (\frac{x}{1 + x})

sum from n=4 to infinity of 1/(n^4)

n = 4 \sum \infty \frac{1}{n ^{4}}

tangent y=2xe^x,(0,0)

t an g e n t y = 2 x e^{x}, (0, 0)

integral of sin(ln(x^2))

\int sin (ln (x^{2})) d x