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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

t an g e n t 2 x + x^{2} - 5, at x = 1

n or ma l y = \frac{x}{4 + x ^{2}}, (0, 0)

\int \frac{x ^{2} - 8}{x ^{4}} d x

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