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Beliebt Rechnen >

(\partial)/(\partial x)((53)/(5+x^2+y^2))

Lösung

\frac{\partial}{\partial x} (\frac{53}{5 + x ^{2} + y ^{2}})

Lösung

- \frac{106 x}{( 5 + x ^{2} + y ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{53}{5 + x ^{2} + y ^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 53 \frac{\partial}{\partial x} (\frac{1}{5 + x ^{2} + y ^{2}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= 53 \frac{\partial}{\partial x} ((5 + x^{2} + y^{2})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 5 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (5 + x^{2} + y^{2})

= - \frac{1}{( 5 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (5 + x^{2} + y^{2})

\frac{\partial}{\partial x} (5 + x^{2} + y^{2}) = 2 x

= 53 (- \frac{1}{( 5 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Vereinfache

53 (- \frac{1}{( 5 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{106 x}{( 5 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{106 x}{( 5 + x ^{2} + y ^{2} ) ^{2}}

Beliebte Beispiele

limit as x approaches 1 of sin(2x)

x \to 1 lim (sin (2 x))

derivative of 5sin(pix)

\frac{d}{d x} (5 sin (π x))

derivative of (x^3/3-4x+1)

\frac{d}{d x} (\frac{x ^{3}}{3} - 4 x + 1)

y^{''}-y^'+1/4 y=3+e^{x/2}

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 3 + e^{\frac{x}{2}}

derivative of sqrt(4x^3+2)

\frac{d}{d x} (4 x^{3} + 2)