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Beliebt Rechnen >

derivative x^4ln(x)

Lösung

ableitung von

x^{4} ln (x)

Lösung

4 x^{3} ln (x) + x^{3}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{4}, g = ln (x)

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} ln (x) + \frac{1}{x} x^{4}

\frac{1}{x} x^{4} = x^{3}

= 4 x^{3} ln (x) + x^{3}

Graph

Beliebte Beispiele

4y^{''}-8y^'+7y=0

4 y^{^{''}} - 8 y^{^{'}} + 7 y = 0

y^{''}+64y=sec^2(8x)

y^{^{''}} + 64 y = sec^{2} (8 x)

integral of cos(4x+1)

\int cos (4 x + 1) d x

integral of tan^3(1)

\int tan^{3} (1) d x

derivative of a*b^x

\frac{d}{d x} (a \cdot b^{x})