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Beliebt Rechnen >

derivative [x+(x+sin^2(x))^3]^6

Lösung

ableitung von

[x + (x + sin^{2} (x))^{3}]^{6}

Lösung

6 (x + (x + sin^{2} (x))^{3})^{5} (1 + 3 (x + sin^{2} (x))^{2} (1 + sin (2 x)))

Schritte zur Lösung

\frac{d}{d x} ((x + (x + sin^{2} (x))^{3})^{6})

Wende die Kettenregel an:

6 (x + (x + sin^{2} (x))^{3})^{5} \frac{d}{d x} (x + (x + sin^{2} (x))^{3})

= 6 (x + (x + sin^{2} (x))^{3})^{5} \frac{d}{d x} (x + (x + sin^{2} (x))^{3})

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

= 6 (x + (x + sin^{2} (x))^{3})^{5} (1 + 3 (x + sin^{2} (x))^{2} (1 + sin (2 x)))

Graph

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