derivative of sin^3(x^2-1)

Lösung

\frac{d}{d x} (sin^{3} (x^{2} - 1))

6 x sin^{2} (x^{2} - 1) cos (x^{2} - 1)

Schritte zur Lösung

\frac{d}{d x} (sin^{3} (x^{2} - 1))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (sin (x^{2} - 1)) = cos (x^{2} - 1) \cdot 2 x

= 3 (sin (x^{2} - 1))^{2} cos (x^{2} - 1) \cdot 2 x

Vereinfache

= 6 x sin^{2} (x^{2} - 1) cos (x^{2} - 1)

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

\frac{d}{d x} (x^{a r c s i n (x)})

\frac{d}{d x} (\frac{4 x + 4 1 + x}{x ^{2} - 1})

\int \frac{8 x ^{2} + 10}{x ^{3} + 5 x} d x

x^{3} = \frac{2 y ^{5} + 4}{5 y ^{4} y ^{^{'}}}