derivative of ((3x-1/(x^2+3))^2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int_{1}^{2} \frac{1}{t} d t

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

\int e^{x} + sin (y) d x

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

x \to - 1 lim (\frac{1}{1 + x ^{2}})