derivative 4(x+2)^{3/2}

Lösung

ableitung von

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

6 (x + 2)^{\frac{1}{2}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= 6 (x + 2)^{\frac{1}{2}}

\frac{d}{d x} ((sin (x) + cos (x)) sec (x))

t an g e n t f (x) = 5 x + 4, at x = 1

\frac{d}{d x} (arctan (x) + arccos (x))

x \to \infty lim (4 x + 5)

t an g e n t f (x) = \frac{2}{x}, at x = 2