derivative of (x^2+3/(sqrt(x^2+1)))

Lösung

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} + 1})

\frac{x ^{3} - x}{( x ^{2} + 1 ) x ^{2} + 1}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} + 3 ) x ^{2} + 1 - \frac{d}{d x} ( x ^{2} + 1 ) ( x ^{2} + 3 )}{( x ^{2} + 1 ) ^{2}}

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

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

= \frac{2 x x ^{2} + 1 - \frac{x}{x ^{2} + 1} ( x ^{2} + 3 )}{( x ^{2} + 1 ) ^{2}}

Vereinfache

\frac{2 x x ^{2} + 1 - \frac{x}{x ^{2} + 1} ( x ^{2} + 3 )}{( x ^{2} + 1 ) ^{2}} : \frac{x ^{3} - x}{( x ^{2} + 1 ) x ^{2} + 1}

= \frac{x ^{3} - x}{( x ^{2} + 1 ) x ^{2} + 1}

\frac{\partial}{\partial y} (\frac{x ^{2}}{4 - y ^{2}})

\frac{\partial}{\partial p} (\frac{p + q}{p + r})

d er i v a t i v e \frac{1}{d + k e ^{d}}

\frac{d ^{2}}{d x ^{2}} y + 36 y = 0

\frac{\partial}{\partial x} (5 e^{x y})