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Beliebt Rechnen >

(\partial)/(\partial x)((x^2-2y)/(4x^2+2y))

Lösung

\frac{\partial}{\partial x} (\frac{x ^{2} - 2 y}{4 x ^{2} + 2 y})

Lösung

\frac{5 x y}{( 2 x ^{2} + y ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x ^{2} - 2 y}{4 x ^{2} + 2 y})

Behandle

y

als Konstante

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{\partial}{\partial x} ( x ^{2} - 2 y ) ( 4 x ^{2} + 2 y ) - \frac{\partial}{\partial x} ( 4 x ^{2} + 2 y ) ( x ^{2} - 2 y )}{( 4 x ^{2} + 2 y ) ^{2}}

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

\frac{\partial}{\partial x} (4 x^{2} + 2 y) = 8 x

= \frac{2 x ( 4 x ^{2} + 2 y ) - 8 x ( x ^{2} - 2 y )}{( 4 x ^{2} + 2 y ) ^{2}}

Vereinfache

\frac{2 x ( 4 x ^{2} + 2 y ) - 8 x ( x ^{2} - 2 y )}{( 4 x ^{2} + 2 y ) ^{2}} : \frac{5 x y}{( 2 x ^{2} + y ) ^{2}}

= \frac{5 x y}{( 2 x ^{2} + y ) ^{2}}

Beliebte Beispiele

(\partial)/(\partial y)(xy^4)

\frac{\partial}{\partial y} (x y^{4})

tangent f(x)=x^3-3x+2,\at x=4

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

fläche y= 1/x ,y=2x-1,0,3

a re a y = \frac{1}{x}, y = 2 x - 1, 0, 3

limit as x approaches infinity of 4cos(3x)

x \to \infty lim (4 cos (3 x))

integral of 0.55t^2+1.575t^4

\int 0.55 t^{2} + 1.575 t^{4} d t