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Beliebt Rechnen >

(\partial)/(\partial x)((7x)/(x^2+y^2))

Lösung

\frac{\partial}{\partial x} (\frac{7 x}{x ^{2} + y ^{2}})

Lösung

\frac{7 ( - x ^{2} + y ^{2} )}{( x ^{2} + y ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{7 x}{x ^{2} + y ^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{2}})

Wende die Quotientenregel an:

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

= 7 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( x ^{2} + y ^{2} ) - \frac{\partial}{\partial x} ( x ^{2} + y ^{2} ) x}{( x ^{2} + y ^{2} ) ^{2}}

\frac{\partial}{\partial x} (x) = 1

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

= 7 \cdot \frac{1 \cdot ( x ^{2} + y ^{2} ) - 2 xx}{( x ^{2} + y ^{2} ) ^{2}}

Vereinfache

7 \cdot \frac{1 \cdot ( x ^{2} + y ^{2} ) - 2 xx}{( x ^{2} + y ^{2} ) ^{2}} : \frac{7 ( - x ^{2} + y ^{2} )}{( x ^{2} + y ^{2} ) ^{2}}

= \frac{7 ( - x ^{2} + y ^{2} )}{( x ^{2} + y ^{2} ) ^{2}}

Beliebte Beispiele

laplacetransform sin(6(t-(5pi)/6))

l a pl a ce t r an s f or m sin (6 (t - \frac{5 π}{6}))

inverselaplace 1/(s(1+s))

in v erse l a pl a ce \frac{1}{s ( 1 + s )}

fläche y=x,y= x/3 ,y=2

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

integral from 0 to 2 of x^2sqrt(1+x^3)

\int_{0}^{2} x^{2} 1 + x^{3} d x

derivative of 2/(1+4x^2)

\frac{d}{d x} (\frac{2}{1 + 4 x ^{2}})