derivative f(x)=(x^2+3)/(x^2)

Lösung

ableitung von

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

- \frac{6}{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) = 2 x

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

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

Vereinfache

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

= - \frac{6}{x ^{3}}

d er i v a t i v e y = cos^{2} (3 x - 1)

x \to 0 - lim (\frac{8}{5 x ^{\frac{1}{2}}})

s l o p e (5.4) (7.7)

\int \frac{x ^{2}}{( 15 + 6 x - 9 x ^{2} ) ^{\frac{3}{2}}} d x

t an g e n t f (x) = x + 1, at x = 0