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

Lösung

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

\frac{2 x ^{3} - 3 x}{2 x ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{2 x ^{3} - 3 x}{2 x ^{3}}

d er i v a t i v e x 18 - x^{2}

l a pl a ce t r an s f or m t e^{3 t}

t an g e n t f (x) = \frac{1}{x - 8}, (- 1, - \frac{1}{9})

\frac{d}{d x} (e^{- 3 x} cos (2 x))

\int \frac{9}{25 + 16 r ^{2}} d r