derivative 1/((x+1)^2)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e (2 x^{2} + x + 1)^{- 3}

\frac{d y}{d t} = \frac{( 2 y ^{4} + t ^{4} )}{t y ^{3}}

\frac{d y}{d t} + 20 \frac{6}{5} - \frac{6}{5} e^{- 20 t} = 24

\int \frac{tan ^{2} ( x )}{sec ( x )} d x