derivative sin^5(x^3)

Lösung

ableitung von

sin^{5} (x^{3})

15 x^{2} sin^{4} (x^{3}) cos (x^{3})

Schritte zur Lösung

\frac{d}{d x} (sin^{5} (x^{3}))

Wende die Kettenregel an:

5 (sin (x^{3}))^{4} \frac{d}{d x} (sin (x^{3}))

= 5 (sin (x^{3}))^{4} \frac{d}{d x} (sin (x^{3}))

\frac{d}{d x} (sin (x^{3})) = cos (x^{3}) \cdot 3 x^{2}

= 5 (sin (x^{3}))^{4} cos (x^{3}) \cdot 3 x^{2}

Vereinfache

= 15 x^{2} sin^{4} (x^{3}) cos (x^{3})

x \to 5 lim (∣ x - 5 ∣)

\int - \frac{2}{100 - 9 t ^{2}} d t

\frac{\partial}{\partial x} (x^{2} + y^{2} - 5)

t an g e n t f (x) = x^{3} - x, at x = 1

\int \frac{1}{5 + 4 x - x ^{2}} d x