derivative of (2x^3-7/(x^2))

Lösung

\frac{d}{d x} (\frac{2 x ^{3} - 7}{x ^{2}})

\frac{2 ( x ^{3} + 7 )}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{3} - 7}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x ^{3} - 7 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 2 x ^{3} - 7 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (2 x^{3} - 7) = 6 x^{2}

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

= \frac{6 x ^{2} x ^{2} - 2 x ( 2 x ^{3} - 7 )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{6 x ^{2} x ^{2} - 2 x ( 2 x ^{3} - 7 )}{( x ^{2} ) ^{2}} : \frac{2 ( x ^{3} + 7 )}{x ^{3}}

= \frac{2 ( x ^{3} + 7 )}{x ^{3}}

t an g e n t y = 3 x^{2} - x^{3}, (1, 2)

\int - \frac{1}{4} csc (8 t) d t

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

\int \frac{11 - 2 x}{x ^{2} + 9 x + 14} d x

x \to 3 lim ((x^{2} - 9)^{x - 3})