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Beliebt Rechnen >

d/(d{x)}({x}^2+{y}^2+{z}^2+{x}{y})

Lösung

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

Lösung

2 x + y

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d}{d x} (z^{2}) = 0

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

= 2 x + 0 + 0 + y

Vereinfache

= 2 x + y

Beliebte Beispiele

xy^2+3y^2-x^2y^'=0

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

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

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

integral of 1/(t^{3/2)}

\int \frac{1}{t ^{\frac{3}{2}}} d t

integral of 2/(1+4x^2)

\int \frac{2}{1 + 4 x ^{2}} d x

integral of sin(1/2)

\int sin (\frac{1}{2})