(\partial)/(\partial x)(x/(1-x^2y^2))

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

t an g e n t y = x^{2} + 4

d er i v a t i v e f (x^{3} - x)

\frac{\partial}{\partial y} (cos (y) + y e^{x})

\int 4 sec (4 x) tan (4 x) d x

t an g e n t x + 9, at x = 7