derivative of x/(sqrt(5-x^2))

Lösung

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

\frac{5}{( 5 - x ^{2} ) 5 - x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} 5 - x ^{2} - \frac{d}{d x} ( 5 - x ^{2} ) x}{( 5 - x ^{2} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (5 - x^{2}) = - \frac{x}{5 - x ^{2}}

= \frac{1 \cdot 5 - x ^{2} - ( - \frac{x}{5 - x ^{2}} ) x}{( 5 - x ^{2} ) ^{2}}

Vereinfache

\frac{1 \cdot 5 - x ^{2} - ( - \frac{x}{5 - x ^{2}} ) x}{( 5 - x ^{2} ) ^{2}} : \frac{5}{( 5 - x ^{2} ) 5 - x ^{2}}

= \frac{5}{( 5 - x ^{2} ) 5 - x ^{2}}

\frac{\partial}{\partial x} (A e^{x})

x \to 4 - lim (\frac{1}{x ^{3} - 64})

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

y^{^{''}} = (\frac{t}{t - 1}) y^{^{'}}

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