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Beliebt Rechnen >

(\partial)/(\partial x)((4x-6y)/(y^2+2x^2))

Lösung

\frac{\partial}{\partial x} (\frac{4 x - 6 y}{y ^{2} + 2 x ^{2}})

Lösung

\frac{4 y ^{2} - 8 x ^{2} + 24 x y}{( y ^{2} + 2 x ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{4 x - 6 y}{y ^{2} + 2 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} ( 4 x - 6 y ) ( y ^{2} + 2 x ^{2} ) - \frac{\partial}{\partial x} ( y ^{2} + 2 x ^{2} ) ( 4 x - 6 y )}{( y ^{2} + 2 x ^{2} ) ^{2}}

\frac{\partial}{\partial x} (4 x - 6 y) = 4

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

= \frac{4 ( y ^{2} + 2 x ^{2} ) - 4 x ( 4 x - 6 y )}{( y ^{2} + 2 x ^{2} ) ^{2}}

Multipliziere aus

4 (y^{2} + 2 x^{2}) - 4 x (4 x - 6 y) : 4 y^{2} - 8 x^{2} + 24 x y

= \frac{4 y ^{2} - 8 x ^{2} + 24 x y}{( y ^{2} + 2 x ^{2} ) ^{2}}

Beliebte Beispiele

derivative of sin(ln(cos(x)))

\frac{d}{d x} (sin (ln (cos (x))))

derivative of (5x^2-9x+13/(2x+4))

\frac{d}{d x} (\frac{5 x ^{2} - 9 x + 13}{2 x + 4})

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x \to 6 lim (\frac{6 + x}{x})

integral of (2x^3-1)/(x+x^4)

\int \frac{2 x ^{3} - 1}{x + x ^{4}} d x

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d er i v a t i v e f (x) = tan^{2} (x^{3})