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

Lösung

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

\frac{3 x ( 2 x ^{2} + 3 )}{( 1 - x ^{2} ) ^{\frac{7}{2}}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

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

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

Vereinfache

\frac{4 x ( 1 - x ^{2} ) ^{\frac{5}{2}} - ( - 5 x ( 1 - x ^{2} ) ^{\frac{3}{2}} ) ( 2 x ^{2} + 1 )}{( ( 1 - x ^{2} ) ^{\frac{5}{2}} ) ^{2}} : \frac{3 x ( 2 x ^{2} + 3 )}{( 1 - x ^{2} ) ^{\frac{7}{2}}}

= \frac{3 x ( 2 x ^{2} + 3 )}{( 1 - x ^{2} ) ^{\frac{7}{2}}}

\int \frac{1}{2 \cdot tan ( x )} d x

\int \frac{x}{x + 3 x} d x

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{9}{x ^{4}}) (x + 5 x^{3}))

x \to 0 lim (2 e^{3 x})

t an g e n t f (x) = \frac{12 x}{x ^{2} - 4}, (4, 4)