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Beliebt Rechnen >

derivative f(x)=arcsin(x^2)

Lösung

ableitung von

f (x) = arcsin (x^{2})

Lösung

\frac{2 x}{1 - x ^{4}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

Vereinfache

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

= \frac{2 x}{1 - x ^{4}}

Graph

Beliebte Beispiele

derivative of (5x-3/(4x-3/x))

\frac{d}{d x} (\frac{5 x - 3}{4 x - \frac{3}{x}})

integral of (2x+3)

\int (2 x + 3) d x

(\partial)/(\partial x)(xy^2+2x^2z)

\frac{\partial}{\partial x} (x y^{2} + 2 x^{2} z)

integral of (x^4-5x^3+7x)/x

\int \frac{x ^{4} - 5 x ^{3} + 7 x}{x} d x

limit as x approaches 6 of (g(x))/(f(x))

x \to 6 lim (\frac{g ( x )}{f ( x )})