derivative of (x^2/((1-y^2)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

\int (\frac{y ^{2}}{4})^{2} d y

\int \frac{1}{10 ( x + 2 )} d x

\int 4 cot^{3} (x) csc^{3} (x) d x

t an g e n t y = 5 2 x^{3} + 8 x, (2, 2)

x \to 0 lim (\frac{sin ( 0 )}{0})