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Beliebt Rechnen >

(\partial)/(\partial x)((42)/((5+x^2+y^2)))

Lösung

\frac{\partial}{\partial x} (\frac{42}{( 5 + x ^{2} + y ^{2} )})

Lösung

- \frac{84 x}{( 5 + x ^{2} + y ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{42}{( 5 + x ^{2} + y ^{2} )})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 42 \frac{\partial}{\partial x} (\frac{1}{5 + x ^{2} + y ^{2}})

Wende Exponentenregel an:

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

= 42 \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

= 42 (- \frac{1}{( 5 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Vereinfache

42 (- \frac{1}{( 5 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{84 x}{( 5 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{84 x}{( 5 + x ^{2} + y ^{2} ) ^{2}}

Beliebte Beispiele

integral of 1/(1+cos(2x))

\int \frac{1}{1 + cos ( 2 x )} d x

integral of x(x^2+1)^5

\int x (x^{2} + 1)^{5} d x

fläche x=3y^2,x=4+2y^2

a re a x = 3 y^{2}, x = 4 + 2 y^{2}

limit as x approaches-4 of x^2-3

x \to - 4 lim (x^{2} - 3)

x^2y^{''}+3xy^'-24y=0

x^{2} y^{^{''}} + 3 x y^{^{'}} - 24 y = 0