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Beliebt Rechnen >

derivative of arcsin(3x^4)

Lösung

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

Lösung

\frac{12 x ^{3}}{1 - 9 x ^{8}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (3 x^{4}) = 12 x^{3}

= \frac{1}{1 - ( 3 x ^{4} ) ^{2}} \cdot 12 x^{3}

Vereinfache

\frac{1}{1 - ( 3 x ^{4} ) ^{2}} \cdot 12 x^{3} : \frac{12 x ^{3}}{1 - 9 x ^{8}}

= \frac{12 x ^{3}}{1 - 9 x ^{8}}

Graph

Beliebte Beispiele

(dy)/(dx)=(6y^3)/((3-2x)^2),y(0)=-1

\frac{d y}{d x} = \frac{6 y ^{3}}{( 3 - 2 x ) ^{2}}, y (0) = - 1

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