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

Lösung

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

\frac{3 ( 2 x ^{5} + 3 x ) - 20}{2 x ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{3 ( 2 x ^{5} + 3 x ) - 20}{2 x ^{3}}

\int_{- 3}^{3} (x + 2) d x

\int_{- 1}^{1} x sin (nπ x) d x

\frac{\partial}{\partial t} (e^{- π t})

\frac{d}{d x} (tan (e^{7 x}) + e^{t a n (7 x)})

y^{^{'}} = 4 y + x^{2} + 7