d/(d{x)}(({z}(x))({x}{y}+{y}ln({x}{y})))

Lösung

\frac{d}{d x} ((z (x)) (x y + y ln (x y)))

z (x) (y + \frac{y}{x})

Schritte zur Lösung

\frac{d}{d x} ((z (x)) (x y + y ln (x y)))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= z (x) \frac{d}{d x} (x y + y ln (x y))

Wende die Summen-/Differenzregel an:

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

= z (x) (\frac{d}{d x} (x y) + \frac{d}{d x} (y ln (x y)))

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

\frac{d}{d x} (y ln (x y)) = \frac{y}{x}

= z (x) (y + \frac{y}{x})

s im pl i f y 3 (2 + 2)

e x p an d \frac{- 2 \cdot x ^{2} + 1}{( x ^{2} + 1 ) ^{\frac{5}{2}}}

e x p an d (10 x - 3 y = 3, 6) - (2 x + 5 y = - 4)

e x p an d \frac{6 e ^{- 5 π s} s + 1 - e ^{- 14 s} + 48 s}{s ( s ^{2} + 64 )}

e x p an d \frac{( x - 2 ) ^{2}}{16}