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

Lösung

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

\frac{6 x ( 2 x ^{2} - 1 ) ^{2}}{( 1 - x ^{2} ) ^{4}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

3 (\frac{2 x ^{2} - 1}{1 - x ^{2}})^{2} \frac{2 x}{( 1 - x ^{2} ) ^{2}} : \frac{6 x ( 2 x ^{2} - 1 ) ^{2}}{( 1 - x ^{2} ) ^{4}}

= \frac{6 x ( 2 x ^{2} - 1 ) ^{2}}{( 1 - x ^{2} ) ^{4}}

y^{^{'}} + 3 y = 2 - 3 e^{- x}

x \to 69 lim (\frac{x - 69}{x - 69})

\int \frac{34}{34 + e ^{x}} d x

\int_{1}^{2} (x - 1) ln (x) d x

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