derivative of 1/(sqrt(x)+1/(sqrt(y)))

Lösung

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

- \frac{1}{2 x ^{\frac{3}{2}}} - \frac{\frac{d y}{d x}}{2 y ^{\frac{3}{2}}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{2 x ^{\frac{3}{2}}}

\frac{d}{d x} (\frac{1}{y}) = - \frac{\frac{d y}{d x}}{2 y ^{\frac{3}{2}}}

= - \frac{1}{2 x ^{\frac{3}{2}}} - \frac{\frac{d y}{d x}}{2 y ^{\frac{3}{2}}}

t an g e n t f (x) = 5 e^{x} + x, at x = 0

\frac{d}{d x} (\frac{- e ^{- \frac{x}{2}} x + e ^{- \frac{x}{2}}}{2})

\frac{d y}{d x} = - 7 e^{x + y}

\int cos (x) x d x

n = 0 \sum \infty \frac{1}{e ^{n^{2}}}