derivative of (a+bx^2/(x^2))

Lösung

\frac{d}{d x} (\frac{a + b x ^{2}}{x ^{2}})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{a + b x ^{2}}{x ^{2}})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{( x ^{4} )}{12} + \frac{( x ^{3} )}{3})

x \to 0 lim (tan^{x} (5 x))

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

\int 4 sin (x) + 3 cos (x) + 5 e^{x} d x

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