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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

= 2 y^{2} \frac{1 \cdot ( x ^{2} + y ^{4} ) - 2 xx}{( x ^{2} + y ^{4} ) ^{2}}

Vereinfache

2 y^{2} \frac{1 \cdot ( x ^{2} + y ^{4} ) - 2 xx}{( x ^{2} + y ^{4} ) ^{2}} : \frac{2 y ^{2} ( - x ^{2} + y ^{4} )}{( x ^{2} + y ^{4} ) ^{2}}

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

Beliebte Beispiele

integral of (7x+4)/(x^3+4x^2)

\int \frac{7 x + 4}{x ^{3} + 4 x ^{2}} d x

y^'+3(tan(3x))y=7cos(3x)

y^{^{'}} + 3 (tan (3 x)) y = 7 cos (3 x)

limit as x approaches 1 of (1-x)^{ln(x)}

x \to 1 lim ((1 - x)^{l n (x)})

integral from 1 to 5 of 4x^2ln(x)

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f^'(x)=2sin(6x),f(pi/6)=-5/2

f^{^{'}} (x) = 2 sin (6 x), f (\frac{π}{6}) = - \frac{5}{2}