d/(dy)(yln(y))

Lösung

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

ln (y) + 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = y, g = ln (y)

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

\frac{d y}{d y} = 1

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

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

Vereinfache

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

= ln (y) + 1

t an g e n t f (x) = 6 e^{x} cos (x), (0, 6)

\frac{\partial}{\partial x} (cos (x^{2} + x y))

n = 3 \sum \infty \frac{6}{n ^{2} - 1}

im pl i c i t x^{5} + y^{5} = 10

x \to 0 - lim (\frac{1}{13 x})