derivative of 1/(x+y^2)

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{1}{2 x + 1})

d er i v a t i v e f (t) = 9 t sin (π t)

\int \frac{cos ( ln ( 9 x ) )}{x} d x

n = 1 \sum \infty \frac{2}{n ( n + 3 )}

x \to 5 lim (4 x - 3 x^{2})