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Beliebt Rechnen >

(\partial)/(\partial x)(4x^3y^2-4x^2+y^6+1)

Lösung

\frac{\partial}{\partial x} (4 x^{3} y^{2} - 4 x^{2} + y^{6} + 1)

Lösung

12 x^{2} y^{2} - 8 x

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x^{3} y^{2} - 4 x^{2} + y^{6} + 1)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (4 x^{3} y^{2}) - \frac{\partial}{\partial x} (4 x^{2}) + \frac{\partial}{\partial x} (y^{6}) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (4 x^{3} y^{2}) = 12 y^{2} x^{2}

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

\frac{\partial}{\partial x} (y^{6}) = 0

\frac{\partial}{\partial x} (1) = 0

= 12 y^{2} x^{2} - 8 x + 0 + 0

Vereinfache

= 12 x^{2} y^{2} - 8 x

Beliebte Beispiele

integral from 2 to 6 of x^2

\int_{2}^{6} x^{2} d x

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

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

(\partial)/(\partial x)(sqrt(9-2x^2-y^2))

\frac{\partial}{\partial x} (9 - 2 x^{2} - y^{2})

integral of 1/4 sin(2x)

\int \frac{1}{4} sin (2 x) d x

integral of x^3sqrt(x^4+11)

\int x^{3} x^{4} + 11 d x