derivative of (3x^3+4(x^4-2x))

Lösung

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

21 x^{6} - 8 x^{3} - 8

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 3 x^{3} + 4, g = x^{4} - 2 x

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

\frac{d}{d x} (3 x^{3} + 4) = 9 x^{2}

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

= 9 x^{2} (x^{4} - 2 x) + (4 x^{3} - 2) (3 x^{3} + 4)

Vereinfache

9 x^{2} (x^{4} - 2 x) + (4 x^{3} - 2) (3 x^{3} + 4) : 21 x^{6} - 8 x^{3} - 8

= 21 x^{6} - 8 x^{3} - 8

x \to 0 lim (\frac{x ^{2} ln ( x )}{x})

\frac{\partial}{\partial x} ((y - 2) (arctan (x)))

\frac{d}{d x} (\frac{csc ( x )}{2 ^{x}})

x \to 0 lim (\frac{x ^{2} - 2 x}{x})

\frac{d}{d x} (- sin (5 x))