(\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 ) ( y ^{2} + 6 x ^{2} ) - 12 x ( - x - 7 y )}{( y ^{2} + 6 x ^{2} ) ^{2}}

Vereinfache

\frac{( - 1 ) ( 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}}

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

\int_{0}^{4} \frac{5}{2 x + 1} d x

d er i v a t i v e 3^{t}

ma c l a u r in x \cdot cos (2 x)

s im pl i f y lo g_{5} (x^{2} - 1)