derivative of 3x\sqrt[4]{x^4-2}

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 4 x^{4} - 2

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

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

\frac{\partial}{\partial x} (x sin (2 x))

\frac{\partial}{\partial x} (x e^{\frac{x}{y}})

s l o p e (6, - 12), (10, - 8)

\int \frac{( ( ln ( x ) ) ^{3} )}{x} d x