derivative y=arcsin(6x+1)

Lösung

ableitung von

y = arcsin (6 x + 1)

\frac{6}{- 36 x ^{2} - 12 x}

Schritte zur Lösung

\frac{d}{d x} (arcsin (6 x + 1))

Wende die Kettenregel an:

\frac{1}{1 - ( 6 x + 1 ) ^{2}} \frac{d}{d x} (6 x + 1)

= \frac{1}{1 - ( 6 x + 1 ) ^{2}} \frac{d}{d x} (6 x + 1)

\frac{d}{d x} (6 x + 1) = 6

= \frac{1}{1 - ( 6 x + 1 ) ^{2}} \cdot 6

Vereinfache

\frac{1}{1 - ( 6 x + 1 ) ^{2}} \cdot 6 : \frac{6}{- 36 x ^{2} - 12 x}

= \frac{6}{- 36 x ^{2} - 12 x}

\int \frac{1}{- 2 x ^{2} - 12 x + 32} d x

s im pl i f y ln (\frac{a ^{2} - z ^{2}}{a ^{2} + z ^{2}})

x \to 5 lim (\frac{x - 5}{x - 5})

x \to 1 lim (18 x^{100} - 5)

\int_{1}^{3} (3 x^{2} + 4) d x