derivative f(x)=arctan(x^2)

Lösung

ableitung von

f (x) = arctan (x^{2})

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

Schritte zur Lösung

\frac{d}{d x} (arctan (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}

t an g e n t (ln (x^{2} - 10 x - 10)), at x = 11

(x^{2} + 1) (\frac{d y}{d x}) + 3 x (y - 1) = 0, y (0) = 8

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