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Beliebt Rechnen >

derivative of x^5*ln(x)

Lösung

\frac{d}{d x} (x^{5} \cdot ln (x))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (x^{5} ln (x))

Wende die Produktregel an:

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

f = x^{5}, g = ln (x)

= \frac{d}{d x} (x^{5}) ln (x) + \frac{d}{d x} (ln (x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} ln (x) + \frac{1}{x} x^{5}

\frac{1}{x} x^{5} = x^{4}

= 5 x^{4} ln (x) + x^{4}

Graph

Beliebte Beispiele

derivative of sqrt(x^2-a^2)

\frac{d}{d x} (x^{2} - a^{2})

sum from n=0 to infinity of 1/(3^{n-1)}

n = 0 \sum \infty \frac{1}{3 ^{n - 1}}

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

limit as x approaches 5 of x/(|x-5|)

x \to 5 lim (\frac{x}{∣ x - 5 ∣})

tangent y=x^2-sqrt(x),(1,0)

t an g e n t y = x^{2} - x, (1, 0)