(\partial)/(\partial y)(e^{xy}ln(y))

Lösung

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

e^{x y} x ln (y) + \frac{e ^{x y}}{y}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Produktregel an:

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

f = e^{x y}, g = ln (y)

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

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

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

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

\frac{1}{y} e^{x y} = \frac{e ^{x y}}{y}

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

y^{^{'}} = e^{- 3 x}

x \to 5 lim (\frac{∣ x - 5 ∣}{x - 5})

\int_{1}^{5} x^{2} ln (x) d x

in v erse l a pl a ce 1 - \frac{1}{1 + x}

\frac{d}{d x} (4 x^{2} 5 x + 1)