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Beliebt Rechnen >

derivative of arcsinh(x^2)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (2x)/(x^2-6)

\int \frac{2 x}{x ^{2} - 6} d x

t a y l or ln (x), 8

derivative 1/3 arctan(x/3)

d er i v a t i v e \frac{1}{3} arctan (\frac{x}{3})

derivative of 2e^{-4x^2+3x+7}

\frac{d}{d x} (2 e^{- 4 x^{2} + 3 x + 7})

derivative f(x)= 7/(sqrt(t))

d er i v a t i v e f (x) = \frac{7}{t}