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Beliebt Funktionen >

derivative of xy^2

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = y^{2}

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

\frac{d x}{d x} = 1

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

= 1 \cdot y^{2} + 2 y \frac{d y}{d x} x

Vereinfache

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

Graph

Beliebte Beispiele

extreme f(x)=x^3-x^2-x-10

e x t re m e f (x) = x^{3} - x^{2} - x - 10

extreme f(x)=(5x-2)/(x^2-10x+25)

e x t re m e f (x) = \frac{5 x - 2}{x ^{2} - 10 x + 25}

extreme p(a,c)=a+5+c

e x t re m e p (a, c) = a + 5 + c

extreme f(x,y)=4y^2-6xy

e x t re m e f (x, y) = 4 y^{2} - 6 x y

extreme f(x,y)=x^2+6xy+12y^2-6x+10y-2

e x t re m e f (x, y) = x^{2} + 6 x y + 12 y^{2} - 6 x + 10 y - 2