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Beliebt Rechnen >

(\partial)/(\partial x)(3-3x+4y-4x^2y)

Lösung

\frac{\partial}{\partial x} (3 - 3 x + 4 y - 4 x^{2} y)

Lösung

- 8 x y - 3

Schritte zur Lösung

\frac{\partial}{\partial x} (3 - 3 x + 4 y - 4 x^{2} y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (3) - \frac{\partial}{\partial x} (3 x) + \frac{\partial}{\partial x} (4 y) - \frac{\partial}{\partial x} (4 x^{2} y)

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

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

\frac{\partial}{\partial x} (4 y) = 0

\frac{\partial}{\partial x} (4 x^{2} y) = 8 y x

= 0 - 3 + 0 - 8 y x

Vereinfache

= - 8 x y - 3

Beliebte Beispiele

derivative of (45/(0.01x^2+1))

\frac{d}{d x} (\frac{45}{0.01 x ^{2} + 1})

integral of 3cos(sqrt(10x))

\int 3 cos (10 x) d x

derivative of log_{5}(x^4sqrt(2x^2+9x))

\frac{d}{d x} (lo g_{5} (x^{4} 2 x^{2} + 9 x))

derivative of (2x-1/(3x^2))

\frac{d}{d x} (\frac{2 x - 1}{3 x ^{2}})

xy^'=y+xe^{y/x}

x y^{^{'}} = y + x e^{\frac{y}{x}}