(\partial)/(\partial x)(x-2|x-2/3 y|)

Lösung

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

1 - \frac{2 ( 3 x - 2 y )}{∣ 3 x - 2 y ∣}

Schritte zur Lösung

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

Vereinfache

x - 2 x - \frac{2}{3} y : x - 2 x - \frac{2 y}{3}

= \frac{\partial}{\partial x} (x - 2 x - \frac{2 y}{3})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x) - \frac{\partial}{\partial x} (2 x - \frac{2 y}{3})

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (2 x - \frac{2 y}{3}) = \frac{2 ( 3 x - 2 y )}{∣ 3 x - 2 y ∣}

= 1 - \frac{2 ( 3 x - 2 y )}{∣ 3 x - 2 y ∣}

d er i v a t i v e f (x) = x^{4} + 3 x

ma c l a u r in \frac{1}{1 - 2 x}

(sin (x) + x cos (x))^{^{'}}

\int \frac{2 e ^{2 x}}{e ^{10} - 1} d x

\int \frac{1}{( 121 + x ^{2} ) ^{2}} d x