derivative of 3/((x-4^2))

Lösung

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

- \frac{6}{( x - 4 ) ^{3}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (\frac{1}{( x - 4 ) ^{2}})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x - 4) = 1

= 3 (- \frac{2}{( x - 4 ) ^{3}} \cdot 1)

Vereinfache

3 (- \frac{2}{( x - 4 ) ^{3}} \cdot 1) : - \frac{6}{( x - 4 ) ^{3}}

= - \frac{6}{( x - 4 ) ^{3}}

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

\frac{\partial}{\partial x} (arctan (\frac{x}{3}))

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

x \to 2 lim (\frac{x ^{3} - 8}{2 x})

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