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Beliebt Rechnen >

derivative of (x^5+5/(x^3))

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

fläche 4x^2+10,2x+7,-3,2

a re a 4 x^{2} + 10, 2 x + 7, - 3, 2

derivative of 3x^2+1/(x^2)

\frac{d}{d x} (3 x^{2} + \frac{1}{x ^{2}})

integral of-1/(x-4)

\int - \frac{1}{x - 4} d x

tangent 4x-32sqrt(x),\at x=4

t an g e n t 4 x - 32 x, at x = 4

integral from-1 to 1 of x^4

\int_{- 1}^{1} x^{4} d x