derivative of (9x/((x^2+1)^{3/5)})

Lösung

\frac{d}{d x} (\frac{9 x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

\frac{9 ( - x ^{2} + 5 )}{5 ( x ^{2} + 1 ) ^{\frac{8}{5}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{9 x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{d}{d x} (\frac{x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

Wende die Quotientenregel an:

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

= 9 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 1 ) ^{\frac{3}{5}} - \frac{d}{d x} ( ( x ^{2} + 1 ) ^{\frac{3}{5}} ) x}{( ( x ^{2} + 1 ) ^{\frac{3}{5}} ) ^{2}}

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

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

= 9 \cdot \frac{1 \cdot ( x ^{2} + 1 ) ^{\frac{3}{5}} - \frac{6 x}{5 ( x ^{2} + 1 ) ^{\frac{2}{5}}} x}{( ( x ^{2} + 1 ) ^{\frac{3}{5}} ) ^{2}}

Vereinfache

9 \cdot \frac{1 \cdot ( x ^{2} + 1 ) ^{\frac{3}{5}} - \frac{6 x}{5 ( x ^{2} + 1 ) ^{\frac{2}{5}}} x}{( ( x ^{2} + 1 ) ^{\frac{3}{5}} ) ^{2}} : \frac{9 ( - x ^{2} + 5 )}{5 ( x ^{2} + 1 ) ^{\frac{8}{5}}}

= \frac{9 ( - x ^{2} + 5 )}{5 ( x ^{2} + 1 ) ^{\frac{8}{5}}}

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

\int \frac{x}{a + b x ^{2}} d x

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

\frac{d}{d x} (i n^{4} x)

d er i v a t i v e x^{2} - x + 1