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Beliebt Rechnen >

derivative of x^2+2xy+y^2

Lösung

\frac{d}{d x} (x^{2} + 2 x y + y^{2})

Lösung

2 x + 2 (y + x \frac{d y}{d x}) + 2 y \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (x^{2} + 2 x y + y^{2})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{2}) + \frac{d}{d x} (2 x y) + \frac{d}{d x} (y^{2})

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (2 x y) = 2 (y + x \frac{d y}{d x})

\frac{d}{d x} (y^{2}) = 2 y \frac{d y}{d x}

= 2 x + 2 (y + x \frac{d y}{d x}) + 2 y \frac{d y}{d x}

Beliebte Beispiele

(\partial)/(\partial x)(4sin(x))

\frac{\partial}{\partial x} (4 sin (x))

derivative x^3+2x-1

d er i v a t i v e x^{3} + 2 x - 1

derivative F(x)=7x^6(x^4-7x)

d er i v a t i v e F (x) = 7 x^{6} (x^{4} - 7 x)

derivative of tan(sqrt(3x))

\frac{d}{d x} (tan (3 x))

integral of cos(pix)

\int cos (π x) d x