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Beliebt Rechnen >

(\partial)/(\partial x)((5x-y)/(y^2+3x^2))

Lösung

\frac{\partial}{\partial x} (\frac{5 x - y}{y ^{2} + 3 x ^{2}})

Lösung

\frac{5 y ^{2} - 15 x ^{2} + 6 x y}{( y ^{2} + 3 x ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{5 x - y}{y ^{2} + 3 x ^{2}})

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} ( 5 x - y ) ( y ^{2} + 3 x ^{2} ) - \frac{\partial}{\partial x} ( y ^{2} + 3 x ^{2} ) ( 5 x - y )}{( y ^{2} + 3 x ^{2} ) ^{2}}

\frac{\partial}{\partial x} (5 x - y) = 5

\frac{\partial}{\partial x} (y^{2} + 3 x^{2}) = 6 x

= \frac{5 ( y ^{2} + 3 x ^{2} ) - 6 x ( 5 x - y )}{( y ^{2} + 3 x ^{2} ) ^{2}}

Multipliziere aus

5 (y^{2} + 3 x^{2}) - 6 x (5 x - y) : 5 y^{2} - 15 x^{2} + 6 x y

= \frac{5 y ^{2} - 15 x ^{2} + 6 x y}{( y ^{2} + 3 x ^{2} ) ^{2}}

Beliebte Beispiele

fläche y=(x^3+1)^{-1},x=0,x=1

a re a y = (x^{3} + 1)^{- 1}, x = 0, x = 1

integral of x^2+4x+4

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

integral from 0 to 4 of-x+1

\int_{0}^{4} - x + 1 d x

limit as x approaches infinity of (sqrt(x))/(6+e^x)

x \to \infty lim (\frac{x}{6 + e ^{x}})

integral of ((4-t+t^2)/(t^2))

\int (\frac{4 - t + t ^{2}}{t ^{2}}) d t