d/(dy)((x)(6x+ln(6y)))

Lösung

\frac{d}{d y} ((x) (6 x + ln (6 y)))

\frac{x}{y}

Schritte zur Lösung

\frac{d}{d y} ((x) (6 x + ln (6 y)))

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{d}{d y} (6 x + ln (6 y))

Wende die Summen-/Differenzregel an:

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

= x (\frac{d}{d y} (6 x) + \frac{d}{d y} (ln (6 y)))

\frac{d}{d y} (6 x) = 0

\frac{d}{d y} (ln (6 y)) = \frac{1}{y}

= x (0 + \frac{1}{y})

Vereinfache

x (0 + \frac{1}{y}) : \frac{x}{y}

= \frac{x}{y}

e x p an d e^{4 x} \cdot 4 (x^{2} + 1) - 2 x e^{4 x}

e x p an d H^{2} + (0.1 t + 1)^{2}

e x p an d 12 (5 (0.675) - 4.5 = 36)

e x p an d (x y + 2 x y ln^{2} (y) + y ln (y)) d x

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