(\partial)/(\partial x)((x^2+y^2-7)/(xy))

Lösung

\frac{\partial}{\partial x} (\frac{x ^{2} + y ^{2} - 7}{x y})

\frac{x ^{2} - y ^{2} + 7}{x ^{2} y}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x ^{2} + y ^{2} - 7}{x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= \frac{1}{y} \frac{\partial}{\partial x} (\frac{x ^{2} + y ^{2} - 7}{x})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{y} \cdot \frac{\frac{\partial}{\partial x} ( x ^{2} + y ^{2} - 7 ) x - \frac{\partial}{\partial x} ( x ) ( x ^{2} + y ^{2} - 7 )}{x ^{2}}

\frac{\partial}{\partial x} (x^{2} + y^{2} - 7) = 2 x

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

= \frac{1}{y} \cdot \frac{2 xx - 1 \cdot ( x ^{2} + y ^{2} - 7 )}{x ^{2}}

Vereinfache

\frac{1}{y} \cdot \frac{2 xx - 1 \cdot ( x ^{2} + y ^{2} - 7 )}{x ^{2}} : \frac{x ^{2} - y ^{2} + 7}{x ^{2} y}

= \frac{x ^{2} - y ^{2} + 7}{x ^{2} y}

\frac{d x}{d t} + 3 t^{3} x^{5} + \frac{x}{t} = 0

d er i v a t i v e x^{2} + 8 x - 2

\int \frac{10}{x ^{5}} d x

t y^{^{'}} + 2 y = \frac{2}{1 + t ^{2}}

\int 3 5 - 4 x^{2} (- 8 x) d x