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Beliebt Rechnen >

derivative of y^2x+2yx^3

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (y^{2} x) = 2 x y \frac{d y}{d x} + y^{2}

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

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

Beliebte Beispiele

steigung (0,-2),(2,2)

s l o p e (0, - 2), (2, 2)

integral from 0 to 1 of sqrt(x+16)

\int_{0}^{1} x + 16 d x

taylor sin(x+pi)

t a y l or sin (x + π)

laplacetransform 2e^{-4t}

l a pl a ce t r an s f or m 2 e^{- 4 t}

derivative of ln(y/x)

\frac{d}{d x} (ln (\frac{y}{x}))