derivative (x^5)/(4-x^4)

Lösung

ableitung von

\frac{x ^{5}}{4 - x ^{4}}

\frac{20 x ^{4} - x ^{8}}{( 4 - x ^{4} ) ^{2}}

Schritte zur Lösung

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

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

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

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

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

Vereinfache

\frac{5 x ^{4} ( 4 - x ^{4} ) - ( - 4 x ^{3} ) x ^{5}}{( 4 - x ^{4} ) ^{2}} : \frac{20 x ^{4} - x ^{8}}{( 4 - x ^{4} ) ^{2}}

= \frac{20 x ^{4} - x ^{8}}{( 4 - x ^{4} ) ^{2}}

y^{^{'''}} - 7 y^{^{''}} - 8 y^{^{'}} = 0

t an g e n t f (x) = \frac{2}{x ^{2}}, at x = 1

\frac{d}{d x} (\frac{1}{2} cos^{2} (\frac{x}{2}))

\int x^{3} \cdot cos (x^{2}) d x

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