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Beliebt Rechnen >

derivative x^2sin^6(x)+xcos^{-3}(x)

Lösung

ableitung von

x^{2} sin^{6} (x) + x cos^{- 3} (x)

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Graph

Beliebte Beispiele

derivative of (e^{2x}/(e^{2x)+1})

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

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integral of-7/(sqrt(x^2+16))

\int - \frac{7}{x ^{2} + 16} d x

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t an g e n t f (x) = \frac{1}{2 x}, at x = 64

derivative of cos(x+pi)

\frac{d}{d x} (cos (x + π))