derivative arccos(x^2+3/2 x)

Lösung

ableitung von

arccos (x^{2} + \frac{3}{2} x)

- \frac{4 x + 3}{4 - 4 x ^{4} - 12 x ^{3} - 9 x ^{2}}

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{1}{1 - ( x ^{2} + \frac{3 x}{2} ) ^{2}} (2 x + \frac{3}{2}) : - \frac{4 x + 3}{4 - 4 x ^{4} - 12 x ^{3} - 9 x ^{2}}

= - \frac{4 x + 3}{4 - 4 x ^{4} - 12 x ^{3} - 9 x ^{2}}

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