derivative f(x)=(3x^5-7x^2-4)/(x^2)

Lösung

ableitung von

f (x) = \frac{3 x ^{5} - 7 x ^{2} - 4}{x ^{2}}

\frac{9 x ^{5} + 8}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{5} - 7 x ^{2} - 4}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x ^{5} - 7 x ^{2} - 4 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 3 x ^{5} - 7 x ^{2} - 4 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (3 x^{5} - 7 x^{2} - 4) = 15 x^{4} - 14 x

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

= \frac{( 15 x ^{4} - 14 x ) x ^{2} - 2 x ( 3 x ^{5} - 7 x ^{2} - 4 )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{( 15 x ^{4} - 14 x ) x ^{2} - 2 x ( 3 x ^{5} - 7 x ^{2} - 4 )}{( x ^{2} ) ^{2}} : \frac{9 x ^{5} + 8}{x ^{3}}

= \frac{9 x ^{5} + 8}{x ^{3}}

x \to 0 lim (cot^{3} (x))

\frac{d}{d x} (\frac{tan ( 20 x )}{x ^{\frac{2}{3}} + 3 x})

x \to 0 lim (\frac{x}{ln ( x + 1 )})

\frac{\partial}{\partial x} (\frac{x ^{4} + y ^{4}}{x ^{2} + y ^{2}})

\frac{d}{d x} (5 sin^{3} (x))