derivative of (1+4x^{3/2})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= 6 (4 x + 1)^{\frac{1}{2}}

\int_{0}^{\infty} 2 e^{- 2 x} d x

\int_{- 8}^{8} \frac{1}{3 x} d x

im pl i c i t \frac{d y}{d x}, y = 7 x^{8}

\int 3 x - 4 x d x

x \to 3 lim (lo g_{5} (x))