derivative y=(x^5)/(3-x^4)

Lösung

ableitung von

y = \frac{x ^{5}}{3 - x ^{4}}

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

= \frac{15 x ^{4} - x ^{8}}{( 3 - x ^{4} ) ^{2}}

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

x \to 4 lim (\frac{x - 4}{x ^{2} + 3 x - 28})

x \to \infty lim (\frac{x}{12})

\frac{d}{d x} (\frac{x - 7}{x + 5})

\frac{\partial}{\partial x} (x^{2} yz - x y z^{5})