derivative x*ln(x)

Lösung

ableitung von

x \cdot ln (x)

ln (x) + 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = ln (x)

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

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

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

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

Vereinfache

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

= ln (x) + 1

\int \frac{x ^{2} - x - 1}{x ^{2} ( x - 1 )} d x

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

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = - \frac{1}{2}, y^{^{'}} (0) = - \frac{17}{4}

\frac{d}{d x} (x^{\frac{3}{2}} + 4)

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