derivative of (5-4x^2+x^5/(x^3))

Lösung

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

\frac{2 x ^{5} + 4 x ^{2} - 15}{x ^{4}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (5 - 4 x^{2} + x^{5}) = 5 x^{4} - 8 x

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

= \frac{( 5 x ^{4} - 8 x ) x ^{3} - 3 x ^{2} ( 5 - 4 x ^{2} + x ^{5} )}{( x ^{3} ) ^{2}}

Vereinfache

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

= \frac{2 x ^{5} + 4 x ^{2} - 15}{x ^{4}}

\int \frac{36}{36 + e ^{x}} d x

x \to 4 lim (\frac{3 x}{x - 4})

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

\frac{d}{d x} (\frac{6}{x + 3})

in v erse l a pl a ce \frac{\frac{10}{6}}{s + 6}