derivative y=xarcsin(2x)

Lösung

ableitung von

y = x arcsin (2 x)

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

Schritte zur Lösung

\frac{d}{d x} (x arcsin (2 x))

Wende die Produktregel an:

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

f = x, g = arcsin (2 x)

= \frac{d x}{d x} arcsin (2 x) + \frac{d}{d x} (arcsin (2 x)) x

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

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

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

Vereinfache

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

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

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

\int_{\frac{1}{7}}^{3} 8 x ln (7 x) d x

t an g e n t y = 3 x + 6 cos (x), at (\frac{π}{3})

in v erse l a pl a ce \frac{s}{s ^{2} + 2 s + 3}

d er i v a t i v e f (x) = \frac{2 x ^{3} - 3 x + 1}{x}