derivative of (x^2+4^{-2})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d y}{d t} = b (1 - y) y

x \to - 9 + lim (3 x^{2} - 4 x - 7)

\int sin (θ) (cot (θ) + csc (θ)) d θ

\frac{\partial}{\partial x} (6 x + 6 y^{2})

\frac{d}{d x} (x f (x))