derivative of 2/(xy)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

f^{^{'}} (x) = x^{2} e^{x^{2}}

t an g e n t \frac{3 x}{x + 1}

d er i v a t i v e 2 x^{2} - \frac{1}{16} ln (x)

y = 8 i n^{x} + c

t \to 0 + lim (arctan (\frac{1}{t}))