(\partial)/(\partial x)(A/(x+sqrt(5)x))

Lösung

\frac{\partial}{\partial x} (\frac{A}{x + 5 x})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{A}{x + 5 x})

Entferne die Konstante:

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

= A \frac{\partial}{\partial x} (\frac{1}{x + 5 x})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (x + 5 x) = 1 + 5

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

Vereinfache

A (- \frac{1}{( x + 5 x ) ^{2}} (1 + 5)) : - \frac{( 1 + 5 ) A}{( x + 5 x ) ^{2}}

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

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

\frac{\partial}{\partial y} (x^{\frac{1}{3}} y^{\frac{2}{3}})

\int \frac{x ^{2} + 6 x + 2}{x ^{3} + 9 x ^{2} + 6 x + 9} d x

y^{^{'}} + 0.06 y = 6

n = 1 \sum \infty \frac{( n ! )}{n ^{n}}