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Beliebt Rechnen >

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

Lösung

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

Lösung

3 x^{2} + 2 y

Schritte zur Lösung

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

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

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

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

\frac{\partial}{\partial x} (y^{2}) = 0

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

Vereinfache

= 3 x^{2} + 2 y

Beliebte Beispiele

derivative y= 3/(4x^5)

d er i v a t i v e y = \frac{3}{4 x ^{5}}

tangent y=5+4x^2-2x^3,(2,5)

t an g e n t y = 5 + 4 x^{2} - 2 x^{3}, (2, 5)

x^{^{''}} + a x = 0

16y^{''}+24y^'+9y=0

16 y^{^{''}} + 24 y^{^{'}} + 9 y = 0

integral of 6rsqrt(4-r^2)

\int 6 r 4 - r^{2} d r