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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d ^{2}}{d x ^{2}} (x e^{7 x})

\int \frac{5 x ^{2}}{x ^{2} - 4} d x

n = 1 \sum \infty 0.4 5^{n}

\frac{\partial}{\partial y} (x y^{2} - x^{3} y)

\int 36 - t^{2} d t