derivative of ((x-2^3)/(x^2))

Lösung

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

\frac{( x - 2 ) ^{2} ( x + 4 )}{x ^{3}}

Schritte zur Lösung

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

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

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

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

Vereinfache

\frac{3 ( x - 2 ) ^{2} x ^{2} - 2 x ( x - 2 ) ^{3}}{( x ^{2} ) ^{2}} : \frac{( x - 2 ) ^{2} ( x + 4 )}{x ^{3}}

= \frac{( x - 2 ) ^{2} ( x + 4 )}{x ^{3}}

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

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

t an g e n t f (x) = 7 e^{x} cos (x), at x = 0

x \to 0 lim ((\frac{x - 4}{x + 1})^{x - 2})

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