derivative of arctan(2x^2-4)

Lösung

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

\frac{4 x}{4 x ^{4} - 16 x ^{2} + 17}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{( 2 x ^{2} - 4 ) ^{2} + 1} \cdot 4 x : \frac{4 x}{4 x ^{4} - 16 x ^{2} + 17}

= \frac{4 x}{4 x ^{4} - 16 x ^{2} + 17}

y^{^{''}} - 8 y^{^{'}} + 16 = 0

x \to π lim ((π - x) cot (x))

l a pl a ce t r an s f or m (e^{- 1}) (sin (2 t))

d er i v a t i v e e^{8 x} cos (11 x)

\int X^{- 1} d X