derivative of (x^6/(sqrt(1+x^{12))})

Lösung

\frac{d}{d x} (\frac{x ^{6}}{1 + x ^{12}})

\frac{6 x ^{5}}{( 1 + x ^{12} ) 1 + x ^{12}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{6}}{1 + x ^{12}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{6} ) 1 + x ^{12} - \frac{d}{d x} ( 1 + x ^{12} ) x ^{6}}{( 1 + x ^{12} ) ^{2}}

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d}{d x} (1 + x^{12}) = \frac{6 x ^{11}}{1 + x ^{12}}

= \frac{6 x ^{5} 1 + x ^{12} - \frac{6 x ^{11}}{1 + x ^{12}} x ^{6}}{( 1 + x ^{12} ) ^{2}}

Vereinfache

\frac{6 x ^{5} 1 + x ^{12} - \frac{6 x ^{11}}{1 + x ^{12}} x ^{6}}{( 1 + x ^{12} ) ^{2}} : \frac{6 x ^{5}}{( 1 + x ^{12} ) 1 + x ^{12}}

= \frac{6 x ^{5}}{( 1 + x ^{12} ) 1 + x ^{12}}

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

\frac{\partial}{\partial y} (x^{2} + y^{2} - 25)

\int - 0.04 t d t

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

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