derivative arcsin(1/t)

Lösung

ableitung von

arcsin (\frac{1}{t})

- \frac{t ^{2}}{t ^{2} t ^{2} - 1}

Schritte zur Lösung

\frac{d}{d t} (arcsin (\frac{1}{t}))

Wende die Kettenregel an:

\frac{1}{1 - ( \frac{1}{t} ) ^{2}} \frac{d}{d t} (\frac{1}{t})

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

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

= \frac{1}{1 - ( \frac{1}{t} ) ^{2}} (- \frac{1}{t ^{2}})

Vereinfache

\frac{1}{1 - ( \frac{1}{t} ) ^{2}} (- \frac{1}{t ^{2}}) : - \frac{t ^{2}}{t ^{2} t ^{2} - 1}

= - \frac{t ^{2}}{t ^{2} t ^{2} - 1}

\frac{d}{d x} (sin (4 x - 5))

t an g e n t f (x) = (x^{2} + 36) (2 x + 21), at x = - 4

d er i v a t i v e f (x) = - 4 x^{2}

x \to 0 lim (\frac{sin ( 4 x ) cos ( 3 x )}{7 x})

im pl i c i t \frac{d y}{d x}, 5 cos (x y) = 6 x + 7 y