derivative y=arcsec(x^2+1)

Lösung

ableitung von

y = arcsec (x^{2} + 1)

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

p a r i t y y = ln (x^{3} - 2 x^{2} + 2)

x \to \infty lim (\frac{2}{x} + 1)

\frac{\partial}{\partial x} (x y)

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

t an g e n t y = 7 cos (x), (\frac{π}{3}, 3.5)