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Beliebt Rechnen >

(\partial)/(\partial x)((2xy^2)/(1+x^2y^2))

Lösung

\frac{\partial}{\partial x} (\frac{2 x y ^{2}}{1 + x ^{2} y ^{2}})

Lösung

\frac{2 y ^{2} ( 1 - x ^{2} y ^{2} )}{( 1 + x ^{2} y ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{2 x y ^{2}}{1 + x ^{2} y ^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 2 y^{2} \frac{\partial}{\partial x} (\frac{x}{1 + x ^{2} y ^{2}})

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 ) ( 1 + x ^{2} y ^{2} ) - \frac{\partial}{\partial x} ( 1 + x ^{2} y ^{2} ) x}{( 1 + x ^{2} y ^{2} ) ^{2}}

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

\frac{\partial}{\partial x} (1 + x^{2} y^{2}) = 2 y^{2} x

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

Vereinfache

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

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

Beliebte Beispiele

(d^2y)/(dx^2)-3(dy)/(dx)+2y=0

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 0

x^{''}+9x=27,x(0)=4,x^'(0)=6

x^{^{''}} + 9 x = 27, x (0) = 4, x^{^{'}} (0) = 6

sum from n=1 to infinity of (2n)/(5n-4)

n = 1 \sum \infty \frac{2 n}{5 n - 4}

tangent y=x^3-3x^2+25

t an g e n t y = x^{3} - 3 x^{2} + 25

derivative of arctan(sec(x+tan(x)))

\frac{d}{d x} (arctan (sec (x) + tan (x)))