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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

Vereinfache

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

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

f (x) = cos ((ln (x + 1))^{2} - e^{x^{2}})

\int \frac{10}{x ^{2} + 16} d x

\frac{d}{d x} (\frac{1}{15} cos^{3} (x) (3 cos^{2} (x) - 5))

\int_{4}^{e^{5}} \frac{1}{x} d x

\frac{d ^{3}}{d x ^{3}} (\frac{1}{1 + x})