derivative y=(x^2-16)/(x^2)

Lösung

ableitung von

y = \frac{x ^{2} - 16}{x ^{2}}

\frac{32}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 16}{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} - 16 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{2} - 16 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{2} - 16) = 2 x

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

= \frac{2 x x ^{2} - 2 x ( x ^{2} - 16 )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{2 x x ^{2} - 2 x ( x ^{2} - 16 )}{( x ^{2} ) ^{2}} : \frac{32}{x ^{3}}

= \frac{32}{x ^{3}}

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

\int \frac{2 x ^{3} - x ^{2} + 4 x - 4}{x ^{4} - 4 x ^{2}} d x

\int_{0}^{2} 1 0^{x} d x

\frac{d}{d x} (e^{3 x} - 1 - 3 x)

d er i v a t i v e f (x) = \frac{2 ( - x ^{2} + 1 )}{( x ^{2} + 1 )}