derivative f(x)= 1/(x+4)

Lösung

ableitung von

f (x) = \frac{1}{x + 4}

- \frac{1}{( x + 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x + 4})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

x \to 0 lim (\frac{3}{x})

\frac{\partial}{\partial x} (\frac{61}{7 + x ^{2} + y ^{2}})

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

\frac{d}{d x} (sin (x^{2} + 5))

\frac{d}{d x} (\frac{7 x}{e ^{x}})