derivative of (x^3-4arcsin(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3} - 4, g = arcsin (x)

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

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

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

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

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

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

\frac{d y}{d x} + x e^{x + y} = 0

\int \frac{22}{x ln ( 7 x )} d x

\frac{d}{d x} (x - 2 y)

\int x sin^{3} (x^{2}) cos^{2} (x^{2}) d x

\int x^{2} ln (x) d x