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Beliebt Vorkalkül >

derivative y=x^3ln(x)

Lösung

ableitung von

y = x^{3} ln (x)

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (x^{3} ln (x))

Wende die Produktregel an:

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

f = x^{3}, g = ln (x)

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} ln (x) + \frac{1}{x} x^{3}

\frac{1}{x} x^{3} = x^{2}

= 3 x^{2} ln (x) + x^{2}

Graph

Beliebte Beispiele

derivative y=x^x

d er i v a t i v e y = x^{x}

derivative y=ln(2x)

d er i v a t i v e y = ln (2 x)

cartesian (2,(3pi)/2)

c a r t es ian (2, \frac{3 π}{2})

derivative f(x)=5sqrt(x)e^{x^2-3}

d er i v a t i v e f (x) = 5 x e^{x^{2} - 3}

polar (5,5sqrt(3))

p o l a r (5, 53)