(\partial)/(\partial x)(2x+3e^y+xy)

Lösung

\frac{\partial}{\partial x} (2 x + 3 e^{y} + x y)

y + 2

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x + 3 e^{y} + x y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (2 x) + \frac{\partial}{\partial x} (3 e^{y}) + \frac{\partial}{\partial x} (x y)

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

\frac{\partial}{\partial x} (3 e^{y}) = 0

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

= 2 + 0 + y

Vereinfache

= y + 2

in v erse l a pl a ce \frac{10 s}{( s + 1 ) ( s + 6 )}

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

\int \frac{ln ^{2} ( x )}{3 x} d x

d er i v a t i v e y = ln (1 - x^{2})

\frac{\partial}{\partial y} (2 y^{3} - 6 y + x^{2})