derivative f(x)= 5/(sqrt(x+4))

Lösung

ableitung von

f (x) = \frac{5}{x + 4}

- \frac{5}{2 ( x + 4 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5}{x + 4})

Entferne die Konstante:

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

= 5 \frac{d}{d x} (\frac{1}{x + 4})

Wende Exponentenregel an:

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

= 5 \frac{d}{d x} ((x + 4)^{- \frac{1}{2}})

Wende die Kettenregel an:

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

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

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

= 5 (- \frac{1}{2 ( x + 4 ) ^{\frac{3}{2}}} \cdot 1)

Vereinfache

5 (- \frac{1}{2 ( x + 4 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{5}{2 ( x + 4 ) ^{\frac{3}{2}}}

= - \frac{5}{2 ( x + 4 ) ^{\frac{3}{2}}}

\int_{0}^{t} t^{2} e^{- \frac{t}{4}} d t

\int (x + 6) (3 x - 4) d x

\int_{- 2}^{0} 3 x 4 - x^{2} d x

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

\frac{\partial}{\partial y} (ln (y - 3 x))