(\partial)/(\partial y)(xe^{xy}-2y+1)

Lösung

\frac{\partial}{\partial y} (x e^{x y} - 2 y + 1)

e^{x y} x^{2} - 2

Schritte zur Lösung

\frac{\partial}{\partial y} (x e^{x y} - 2 y + 1)

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (x e^{x y}) - \frac{\partial}{\partial y} (2 y) + \frac{\partial}{\partial y} (1)

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

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

\frac{\partial}{\partial y} (1) = 0

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

Vereinfache

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

t an g e n t ln (x)

\frac{d}{d x} ((x^{2} + y^{2} + z^{2})^{\frac{1}{2}})

\frac{d}{d x} (6 ln (sec (x) + tan (x)))

d er i v a t i v e cos^{3} (x)

y^{^{'}} - \frac{6}{x} y = \frac{y ^{4}}{x ^{15}}