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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{9 ( 1 - 2 x ) ^{2}}{( 1 + x ) ^{4}}

\frac{d}{d x} (\frac{4 x}{7 - tan ( x )})

\int_{0}^{5} \frac{1}{x ^{\frac{17}{16}}} d x

d er i v a t i v e [tan (x^{\frac{2}{3}})]^{3}

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

d er i v a t i v e f (t) = 7 + 10 x