derivative of arccos(2xsqrt(1-x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (e^{- 2 t})

\int \frac{cos ( x )}{2} d x

s l o p e (2.5) (3.7)

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\int \frac{1}{2 + 3 x} d x