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Beliebt Rechnen >

derivative of x^2y+xy^2

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Beliebte Beispiele

integral from 1 to 2 of 2(1-1/(x^2))

\int_{1}^{2} 2 (1 - \frac{1}{x ^{2}}) d x

derivative f(x)= x/(x^2+7)

d er i v a t i v e f (x) = \frac{x}{x ^{2} + 7}

derivative of 3/(4(1-x^{5/2)})

\frac{d}{d x} (\frac{3}{4 ( 1 - x ) ^{\frac{5}{2}}})

4 x^{2} y^{^{''}} + y = 0

integral of (x^2)/6

\int \frac{x ^{2}}{6} d x