derivative sqrt((1-x)^2+x^3)

Lösung

ableitung von

(1 - x)^{2} + x^{3}

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

\int \frac{1}{- 2 x ^{2} + 8 x + 4} d x

\int_{0}^{3} (2 x - x^{2})^{3} (1 - x) d x

\frac{\partial}{\partial x} (z^{2} cos (y x))

y^{^{'}} - \frac{6}{x} y = \frac{( y ^{3} )}{x ^{4}}