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Beliebt Rechnen >

derivative of 3arcsin(x^4)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (2x^3)/(sqrt(1+x^4))

\int \frac{2 x ^{3}}{1 + x ^{4}} d x

integral of (2t-1)/(t^2-2t+1)

\int \frac{2 t - 1}{t ^{2} - 2 t + 1} d t

derivative of-5sin(5x)

\frac{d}{d x} (- 5 sin (5 x))

integral of 1/(usqrt(1+u^2))

\int \frac{1}{u 1 + u ^{2}} d u

derivative of 7sin(337x+(7pi/(18)))

\frac{d}{d x} (7 sin (337 x + \frac{7 π}{18}))