derivative of ((x^3-4x^8)/8)

Lösung

\frac{d}{d x} (\frac{( x ^{3} - 4 x ) ^{8}}{8})

(3 x^{2} - 4) (x^{3} - 4 x)^{7}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x ^{3} - 4 x ) ^{8}}{8})

Entferne die Konstante:

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

= \frac{1}{8} \frac{d}{d x} ((x^{3} - 4 x)^{8})

Wende die Kettenregel an:

8 (x^{3} - 4 x)^{7} \frac{d}{d x} (x^{3} - 4 x)

= 8 (x^{3} - 4 x)^{7} \frac{d}{d x} (x^{3} - 4 x)

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

= \frac{1}{8} \cdot 8 (x^{3} - 4 x)^{7} (3 x^{2} - 4)

Vereinfache

\frac{1}{8} \cdot 8 (x^{3} - 4 x)^{7} (3 x^{2} - 4) : (3 x^{2} - 4) (x^{3} - 4 x)^{7}

= (3 x^{2} - 4) (x^{3} - 4 x)^{7}

x^{2} + 4 x y + x (\frac{d y}{d x}) = 0

\frac{\partial}{\partial x} (y ln (5 x + y))

\int_{1}^{6} 7 \frac{ln ( x )}{x ^{2}} d x

\int sin (2 x) e^{c o s^{2} (x)} d x

x \to 3 lim (\frac{6}{x - 3})