(\partial)/(\partial x)(36(x/(x+y))-x)

Lösung

\frac{\partial}{\partial x} (36 (\frac{x}{x + y}) - x)

\frac{36 y}{( x + y ) ^{2}} - 1

Schritte zur Lösung

\frac{\partial}{\partial x} (36 (\frac{x}{x + y}) - x)

Vereinfache

36 (\frac{x}{x + y}) - x : \frac{36 x}{x + y} - x

= \frac{\partial}{\partial x} (\frac{36 x}{x + y} - x)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (\frac{36 x}{x + y}) - \frac{\partial}{\partial x} (x)

\frac{\partial}{\partial x} (\frac{36 x}{x + y}) = \frac{36 y}{( x + y ) ^{2}}

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

= \frac{36 y}{( x + y ) ^{2}} - 1

(x^{2} + 1) (\frac{d y}{d x}) + 8 x (y - 1) = 0, y (0) = 6

\frac{\partial}{\partial x} (2 x^{3} y + 1)

x \to 5 lim (x + 2)

x \to 2 lim ((x - 1)^{2} - 1)

d er i v a t i v e \frac{x + 2}{10 - 3 x}