derivative of 1/((2x+3^2))

Lösung

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

- \frac{4}{( 2 x + 3 ) ^{3}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{2}{( 2 x + 3 ) ^{3}} \cdot 2 : - \frac{4}{( 2 x + 3 ) ^{3}}

= - \frac{4}{( 2 x + 3 ) ^{3}}

\int sin^{2} (x + 2) d x

\frac{d}{d x} (\frac{- 2}{3 x})

\int 144 - t^{2} d t

\int_{0}^{5} (2 e^{x} + 4 cos (x)) d x

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