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Beliebt Rechnen >

derivative of x^3+y^3-9xy

Lösung

\frac{d}{d x} (x^{3} + y^{3} - 9 x y)

Lösung

3 x^{2} + 3 y^{2} \frac{d y}{d x} - 9 (y + x \frac{d y}{d x})

Schritte zur Lösung

\frac{d}{d x} (x^{3} + y^{3} - 9 x y)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (y^{3}) - \frac{d}{d x} (9 x y)

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

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

\frac{d}{d x} (9 x y) = 9 (y + x \frac{d y}{d x})

= 3 x^{2} + 3 y^{2} \frac{d y}{d x} - 9 (y + x \frac{d y}{d x})

Beliebte Beispiele

integral of 6x^2ln(x)

\int 6 x^{2} ln (x) d x

integral of 1/(9x^2-4)

\int \frac{1}{9 x ^{2} - 4} d x

taylor e^{-x^3}

t a y l or e^{- x^{3}}

integral of x/u

\int \frac{x}{u}

fläche y=x^3,0<= x<= 3

a re a y = x^{3}, 0 \leq x \leq 3