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Beliebt Rechnen >

(\partial)/(\partial x)(x^3+y^3-9xy)

Lösung

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

Lösung

3 x^{2} - 9 y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (y^{3}) = 0

\frac{\partial}{\partial x} (9 x y) = 9 y

= 3 x^{2} + 0 - 9 y

Vereinfache

= 3 x^{2} - 9 y

Beliebte Beispiele

limit as x approaches pi/4 of tan(x)

x \to \frac{π}{4} lim (tan (x))

derivative x/(sqrt(x)+9)

d er i v a t i v e \frac{x}{x + 9}

tangent y=e^{-4t},\at t=0

t an g e n t y = e^{- 4 t}, at t = 0

derivative (1+csc(x^7))/(1-cot(x^7))

d er i v a t i v e \frac{1 + csc ( x ^{7} )}{1 - cot ( x ^{7} )}

integral of (x-1)/(sqrt(x))

\int \frac{x - 1}{x} d x