derivative y=(x^3+x)arcsin(x)

Lösung

ableitung von

y = (x^{3} + x) arcsin (x)

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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

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

p o l a r (5, 0)

s l o p e in t erce pt y = 2 (5 x + 1) + 3 (5 x + 3)

x = 10

s im pl i f y (- 2.3) (10.3)

d er i v a t i v e f (x) = \frac{5}{x}, at x = - 1