derivative of \sqrt[4]{(3x-2/(x^2+1)})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{y ^{^{'}} - e ^{- t} + 4}{y} = - 4, y (0) = - 4

\int x^{3} x^{2} + 45 d x

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

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

\frac{d}{d x} (\frac{1}{sec ^{2} ( x )})