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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

= 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 \cdot \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 x

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

Vereinfache

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

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

Beliebte Beispiele

derivative of x^3-2x-5

\frac{d}{d x} (x^{3} - 2 x - 5)

d/(dt)((\sqrt[3]{t})/(t-6))

\frac{d}{d t} (\frac{3 t}{t - 6})

limit as x approaches 0 of x^4ln(x)

x \to 0 lim (x^{4} ln (x))

steigung (-2.4)(2.4)

s l o p e (- 2.4) (2.4)

(\partial)/(\partial x)(2^{x^2})

\frac{\partial}{\partial x} (2^{x^{2}})