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Beliebt Rechnen >

(\partial)/(\partial y)(yln(y))

Lösung

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

Lösung

ln (y) + 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = y, g = ln (y)

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

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial 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

Beliebte Beispiele

integral of sqrt(x^4+1)

\int x^{4} + 1 d x

integral of e^{9x}cos(2x)

\int e^{9 x} cos (2 x) d x

2t^2((dx)/(dt))=3tx+x^2

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

f (x) = 5 sin (x)

derivative f(x)=e^{-5x^4}

d er i v a t i v e f (x) = e^{- 5 x^{4}}