d/(dy)(1/(1+y^2))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial v} (u + uv)

d er i v a t i v e y = x^{3} - 8 x^{2} + 4 x - 32

\int sin (x) sec (x) d x

\frac{d x}{d t} = a x - b x^{2} - 0

d er i v a t i v e \frac{2 x ^{2} + 4 x + 2}{x}