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Beliebt Rechnen >

derivative of arctan(2x^4)

Lösung

\frac{d}{d x} (arctan (2 x^{4}))

Lösung

\frac{8 x ^{3}}{4 x ^{8} + 1}

Schritte zur Lösung

\frac{d}{d x} (arctan (2 x^{4}))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (2 x^{4}) = 8 x^{3}

= \frac{1}{( 2 x ^{4} ) ^{2} + 1} \cdot 8 x^{3}

Vereinfache

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

= \frac{8 x ^{3}}{4 x ^{8} + 1}

Graph

Beliebte Beispiele

integral of (x^2+3)^42x

\int (x^{2} + 3)^{4} 2 x d x

integral of e^{-ax^2}

\int e^{- a x^{2}} d x

derivative y=2\sqrt[3]{x}

d er i v a t i v e y = 2 3 x

tangent y=(1+4x)^{11},(0,1)

t an g e n t y = (1 + 4 x)^{11}, (0, 1)

tangent f(x)=(sqrt(x))/(x+6),\at x=4

t an g e n t f (x) = \frac{x}{x + 6}, at x = 4