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Beliebt Rechnen >

derivative of 2x^2y^3

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = y^{3}

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

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

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

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

Beliebte Beispiele

integral of (tan(x/6))^5

\int (tan (\frac{x}{6}))^{5} d x

integral of-1/3 e^{-3x}

\int - \frac{1}{3} e^{- 3 x} d x

integral of 1/(sqrt(u^2-16))

\int \frac{1}{u ^{2} - 16} d u

derivative of 4/(x^{10})

\frac{d}{d x} (\frac{4}{x ^{10}})

integral of 1/(sqrt(16-x^2))

\int \frac{1}{16 - x ^{2}} d x