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

Lösung

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

- \frac{14 x y}{( x - y ) ^{3}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

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

Vereinfache

7 \cdot \frac{2 x ( x - y ) ^{2} - 2 ( x - y ) x ^{2}}{( ( x - y ) ^{2} ) ^{2}} : - \frac{14 x y}{( x - y ) ^{3}}

= - \frac{14 x y}{( x - y ) ^{3}}

\int_{1}^{t} \frac{3}{x ^{3}} d x

\int \frac{1}{9 x ^{2} + 4} d x

\int_{- x}^{x} t^{3} d t

\frac{d}{d x} (2 x^{3} - 4 x + 5)

d er i v a t i v e \frac{t}{t - 1}