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Beliebt Rechnen >

derivative of xln(3x)

Lösung

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

Lösung

ln (3 x) + 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = ln (3 x)

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

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

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

Vereinfache

1 \cdot ln (3 x) + \frac{1}{x} x : ln (3 x) + 1

= ln (3 x) + 1

Graph

Beliebte Beispiele

y=(x^3+1)(x^2-2)

y = (x^{3} + 1) (x^{2} - 2)

y^{''}+15y^'-56y=0

y^{^{''}} + 15 y^{^{'}} - 56 y = 0

laplacetransform e^{(-2(t-3))}

l a pl a ce t r an s f or m e^{(- 2 (t - 3))}

integral of (x^4-2x^3+1)/(x^2)

\int \frac{x ^{4} - 2 x ^{3} + 1}{x ^{2}} d x

derivative f(x)=(3x)^{2x}

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