(\partial)/(\partial y)(yln(y)-e^{-xy})

Lösung

\frac{\partial}{\partial y} (y ln (y) - e^{- x y})

ln (y) + 1 + e^{- y x} x

Schritte zur Lösung

\frac{\partial}{\partial y} (y ln (y) - e^{- x y})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (y ln (y)) - \frac{\partial}{\partial y} (e^{- x y})

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

\frac{\partial}{\partial y} (e^{- x y}) = - x e^{- x y}

= ln (y) + 1 - (- x e^{- x y})

Vereinfache

= ln (y) + 1 + e^{- y x} x

\int \frac{3 x + 1}{x ^{2} - 10 x + 28} d x

d er i v a t i v e 200 (e)^{0.03 x}

a re a y = x^{4} - 3 x^{2} + 3, y = x^{2}

\frac{d}{d v} (\frac{3 v - 2 v e ^{v}}{v})

t an g e n t y = 5 x^{2} - x^{3}, (1, 4)