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Beliebt Rechnen >

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

Lösung

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

Lösung

3 x^{2} y^{2} + 3 y - 8 x y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

= 3 y^{2} x^{2} - 8 y x + 3 y - 0

Vereinfache

= 3 x^{2} y^{2} + 3 y - 8 x y

Beliebte Beispiele

tangent y=x^2+5x+6,\at x=7

t an g e n t y = x^{2} + 5 x + 6, at x = 7

integral of sqrt(144-9x^2)

\int 144 - 9 x^{2} d x

limit as x approaches-5+of 3/(x^2-25)

x \to - 5 + lim (\frac{3}{x ^{2} - 25})

derivative of x^{sin(3x})

\frac{d}{d x} (x^{s i n (3 x)})

(\partial)/(\partial u)(cos(u+v))

\frac{\partial}{\partial u} (cos (u + v))