(\partial)/(\partial x)(e^{xy}+2x-5y)

Lösung

\frac{\partial}{\partial x} (e^{x y} + 2 x - 5 y)

e^{x y} y + 2

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{x y} + 2 x - 5 y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (e^{x y}) + \frac{\partial}{\partial x} (2 x) - \frac{\partial}{\partial x} (5 y)

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

\frac{\partial}{\partial x} (2 x) = 2

\frac{\partial}{\partial x} (5 y) = 0

= e^{x y} y + 2 - 0

Vereinfache

= e^{x y} y + 2

y^{^{''}} + 8 y^{^{'}} + 7 y = 0, y (0) = 6, y^{^{'}} (0) = - 1

\frac{d ^{2}}{d x ^{2}} (x^{4} - 6 x^{3})

\frac{\partial}{\partial x} (\frac{7 x}{x ^{2} + y ^{2}})

l a pl a ce t r an s f or m sin (6 (t - \frac{5 π}{6}))

in v erse l a pl a ce \frac{1}{s ( 1 + s )}