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Beliebt Rechnen >

derivative y=3sin(x^3-5x^2+8x+0.5)

Lösung

ableitung von

y = 3 sin (x^{3} - 5 x^{2} + 8 x + 0.5)

Lösung

3 cos (x^{3} - 5 x^{2} + 8 x + 0.5) (3 x^{2} - 10 x + 8)

Schritte zur Lösung

\frac{d}{d x} (3 sin (x^{3} - 5 x^{2} + 8 x + 0.5))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (sin (x^{3} - 5 x^{2} + 8 x + 0.5))

Wende die Kettenregel an:

cos (x^{3} - 5 x^{2} + 8 x + 0.5) \frac{d}{d x} (x^{3} - 5 x^{2} + 8 x + 0.5)

= cos (x^{3} - 5 x^{2} + 8 x + 0.5) \frac{d}{d x} (x^{3} - 5 x^{2} + 8 x + 0.5)

\frac{d}{d x} (x^{3} - 5 x^{2} + 8 x + 0.5) = 3 x^{2} - 10 x + 8

= 3 cos (x^{3} - 5 x^{2} + 8 x + 0.5) (3 x^{2} - 10 x + 8)

Graph

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

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\int \frac{e ^{x}}{e ^{- 6 x}} d x

derivative of (5x/(9x^2+1))

\frac{d}{d x} (\frac{5 x}{9 x ^{2} + 1})

y^{^{'}} = y - k