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Beliebt Rechnen >

derivative-(x+3arcsin(x))/4

Lösung

ableitung von

- \frac{x + 3 arcsin ( x )}{4}

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (- \frac{x + 3 arcsin ( x )}{4})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{4} \frac{d}{d x} (x + 3 arcsin (x))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{1}{4} (\frac{d x}{d x} + \frac{d}{d x} (3 arcsin (x)))

\frac{d x}{d x} = 1

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

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

Graph

Beliebte Beispiele

integral of (4x-10)/(x^2-6x+8)

\int \frac{4 x - 10}{x ^{2} - 6 x + 8} d x

integral of (x+2)/(x+5)

\int \frac{x + 2}{x + 5} d x

f (t) = t^{6}

derivative f(x)=5x^4-5x^2+7

d er i v a t i v e f (x) = 5 x^{4} - 5 x^{2} + 7

integral of 1/(x^2+8x+16)

\int \frac{1}{x ^{2} + 8 x + 16} d x