derivative of x/(1+sqrt(1-x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int \frac{1100 x}{x ^{2} + 80} d x

t an g e n t f (x) = x, (64, 8)

\frac{\partial}{\partial x} (cos (x - y))

d er i v a t i v e f (x) = 2 x + 4

\int 2 x (x^{2} + 9)^{7} d x