derivative of sqrt((5x+1/(2x^2+1)))

Lösung

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

\frac{- 10 x ^{2} - 4 x + 5}{2 5 x + 1 ( 2 x ^{2} + 1 ) ^{\frac{3}{2}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{5 x + 1}{2 x ^{2} + 1}) = \frac{- 10 x ^{2} - 4 x + 5}{( 2 x ^{2} + 1 ) ^{2}}

= \frac{1}{2 \frac{5 x + 1}{2 x ^{2} + 1}} \cdot \frac{- 10 x ^{2} - 4 x + 5}{( 2 x ^{2} + 1 ) ^{2}}

Vereinfache

\frac{1}{2 \frac{5 x + 1}{2 x ^{2} + 1}} \cdot \frac{- 10 x ^{2} - 4 x + 5}{( 2 x ^{2} + 1 ) ^{2}} : \frac{- 10 x ^{2} - 4 x + 5}{2 5 x + 1 ( 2 x ^{2} + 1 ) ^{\frac{3}{2}}}

= \frac{- 10 x ^{2} - 4 x + 5}{2 5 x + 1 ( 2 x ^{2} + 1 ) ^{\frac{3}{2}}}

x \to \infty lim (\frac{3 x ^{2} + 2 x - 8}{4 x ^{4} - 5 x + 4})

x \to 0 lim (\frac{1}{x + 1})

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

\int (6 x^{2} - 4 x + 5) d x

\int \frac{1}{x ^{3} + 9 x} d x