(\partial)/(\partial x)((x-7y)/(y^2+6x^2))

Lösung

\frac{\partial}{\partial x} (\frac{x - 7 y}{y ^{2} + 6 x ^{2}})

\frac{y ^{2} - 6 x ^{2} + 84 x y}{( y ^{2} + 6 x ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x - 7 y}{y ^{2} + 6 x ^{2}})

Behandle

y

als Konstante

Wende die Quotientenregel an:

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

= \frac{\frac{\partial}{\partial x} ( x - 7 y ) ( y ^{2} + 6 x ^{2} ) - \frac{\partial}{\partial x} ( y ^{2} + 6 x ^{2} ) ( x - 7 y )}{( y ^{2} + 6 x ^{2} ) ^{2}}

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

\frac{\partial}{\partial x} (y^{2} + 6 x^{2}) = 12 x

= \frac{1 \cdot ( y ^{2} + 6 x ^{2} ) - 12 x ( x - 7 y )}{( y ^{2} + 6 x ^{2} ) ^{2}}

Vereinfache

\frac{1 \cdot ( y ^{2} + 6 x ^{2} ) - 12 x ( x - 7 y )}{( y ^{2} + 6 x ^{2} ) ^{2}} : \frac{y ^{2} - 6 x ^{2} + 84 x y}{( y ^{2} + 6 x ^{2} ) ^{2}}

= \frac{y ^{2} - 6 x ^{2} + 84 x y}{( y ^{2} + 6 x ^{2} ) ^{2}}

\int x^{2} + x d x

t an g e n t f (x) = 2 x^{2} + 9, at x = 1

\frac{d}{d y} (cos (y))

(- \frac{1}{x ^{2}})^{^{'}}

\frac{d}{d x} (x ln (x^{2}) - 2 x)