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}}

y^{^{''}} + 9 y = 4 tan (3 x)

d er i v a t i v e y = ln^{2} (x + 3)

\frac{\partial}{\partial x} (e^{x^{2} y})

2 y^{^{''}} + 12 y^{^{'}} + 50 y = 0, y (0) = 0, y^{^{'}} (0) = - 8

t an g e n t y = x + 8, (8, 4)