(\partial)/(\partial x)(1/(f(x))-1/x)

Lösung

\frac{\partial}{\partial x} (\frac{1}{f ( x )} - \frac{1}{x})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{f ( x )} - \frac{1}{x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (\frac{1}{f ( x )}) - \frac{\partial}{\partial x} (\frac{1}{x})

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

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

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

Vereinfache

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

\frac{d}{d x} (y^{2} + x^{2})

\int sin (\frac{1}{7}) x d x

h \to 0 lim \frac{( ( h - 5 ) ^{2} - 25 )}{( h )}

\frac{d}{d y} (2 x y^{3})

\int - \frac{1}{s} e^{- s t} d t