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Beliebt Rechnen >

derivative x^2sin^3(x)+xcos^{-3}(x)

Lösung

ableitung von

x^{2} sin^{3} (x) + x cos^{- 3} (x)

Lösung

2 x sin^{3} (x) + 3 sin^{2} (x) cos (x) x^{2} + sec^{3} (x) (1 + 3 x tan (x))

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (x cos^{- 3} (x)) = sec^{3} (x) (1 + 3 x tan (x))

= 2 x sin^{3} (x) + 3 sin^{2} (x) cos (x) x^{2} + sec^{3} (x) (1 + 3 x tan (x))

Graph

Beliebte Beispiele

limit as x approaches infinity of x^2+6

x \to \infty lim (x^{2} + 6)

tangent f(x)=(4x+4)^{1/3},\at x=1

t an g e n t f (x) = (4 x + 4)^{\frac{1}{3}}, at x = 1

integral of 10x-x^2

\int 10 x - x^{2} d x

integral of (x^{2/3}+3)

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

derivative y=arcsin(x/6)

d er i v a t i v e y = arcsin (\frac{x}{6})