derivative x^{11}arcsin(x)

Lösung

ableitung von

x^{11} arcsin (x)

11 x^{10} arcsin (x) + \frac{x ^{11}}{1 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x^{11} arcsin (x))

Wende die Produktregel an:

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

f = x^{11}, g = arcsin (x)

= \frac{d}{d x} (x^{11}) arcsin (x) + \frac{d}{d x} (arcsin (x)) x^{11}

\frac{d}{d x} (x^{11}) = 11 x^{10}

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

= 11 x^{10} arcsin (x) + \frac{1}{1 - x ^{2}} x^{11}

\frac{1}{1 - x ^{2}} x^{11} = \frac{x ^{11}}{1 - x ^{2}}

= 11 x^{10} arcsin (x) + \frac{x ^{11}}{1 - x ^{2}}

2 y (x^{2} + 4)^{2} = \frac{5 x ( y ^{2} + 1 ) ^{2}}{y ^{^{'}} ( x ^{2} + 4 )}

\frac{\partial}{\partial x} (x sin (yz))

y y^{^{'}} + 25 x = 0

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

y^{^{'}} = 2 x - y, y (0) = 1