derivative y=(arcsin(x^3))^4

Lösung

ableitung von

y = (arcsin (x^{3}))^{4}

\frac{12 x ^{2} arcsin ^{3} ( x ^{3} )}{1 - x ^{6}}

Schritte zur Lösung

\frac{d}{d x} ((arcsin (x^{3}))^{4})

Wende die Kettenregel an:

4 (arcsin (x^{3}))^{3} \frac{d}{d x} (arcsin (x^{3}))

= 4 (arcsin (x^{3}))^{3} \frac{d}{d x} (arcsin (x^{3}))

\frac{d}{d x} (arcsin (x^{3})) = \frac{3 x ^{2}}{1 - x ^{6}}

= 4 (arcsin (x^{3}))^{3} \frac{3 x ^{2}}{1 - x ^{6}}

Vereinfache

4 arcsin^{3} (x^{3}) \frac{3 x ^{2}}{1 - x ^{6}} : \frac{12 x ^{2} arcsin ^{3} ( x ^{3} )}{1 - x ^{6}}

= \frac{12 x ^{2} arcsin ^{3} ( x ^{3} )}{1 - x ^{6}}

p er p e n d i c u l a r y = 3 x - 2

mi d p o in t (1, 1), (4, - 16)

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

t an g e n t x

d er i v a t i v e 2 x^{2}