derivative ((5x^5-3x^2+1))/x

Lösung

ableitung von

\frac{( 5 x ^{5} - 3 x ^{2} + 1 )}{x}

\frac{20 x ^{5} - 3 x ^{2} - 1}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 5 x ^{5} - 3 x ^{2} + 1 ) x - \frac{d x}{d x} ( 5 x ^{5} - 3 x ^{2} + 1 )}{x ^{2}}

\frac{d}{d x} (5 x^{5} - 3 x^{2} + 1) = 25 x^{4} - 6 x

\frac{d x}{d x} = 1

= \frac{( 25 x ^{4} - 6 x ) x - 1 \cdot ( 5 x ^{5} - 3 x ^{2} + 1 )}{x ^{2}}

Vereinfache

\frac{( 25 x ^{4} - 6 x ) x - 1 \cdot ( 5 x ^{5} - 3 x ^{2} + 1 )}{x ^{2}} : \frac{20 x ^{5} - 3 x ^{2} - 1}{x ^{2}}

= \frac{20 x ^{5} - 3 x ^{2} - 1}{x ^{2}}

\int \frac{1}{12 ( x ^{2} + 1 )} d x

x \to 3 + lim (\frac{x}{x - 3})

(1 + x) y^{^{'}} - x y = x + x^{2}

\frac{\partial}{\partial y} (x^{2} e^{y^{2}})

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