derivative 10x(x^2+6)^4

Lösung

ableitung von

10 x (x^{2} + 6)^{4}

10 ((x^{2} + 6)^{4} + 8 x^{2} (x^{2} + 6)^{3})

Schritte zur Lösung

\frac{d}{d x} (10 x (x^{2} + 6)^{4})

Entferne die Konstante:

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

= 10 \frac{d}{d x} (x (x^{2} + 6)^{4})

Wende die Produktregel an:

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

f = x, g = (x^{2} + 6)^{4}

= 10 (\frac{d x}{d x} (x^{2} + 6)^{4} + \frac{d}{d x} ((x^{2} + 6)^{4}) x)

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

\frac{d}{d x} ((x^{2} + 6)^{4}) = 8 x (x^{2} + 6)^{3}

= 10 (1 \cdot (x^{2} + 6)^{4} + 8 x (x^{2} + 6)^{3} x)

Vereinfache

10 (1 \cdot (x^{2} + 6)^{4} + 8 x (x^{2} + 6)^{3} x) : 10 ((x^{2} + 6)^{4} + 8 x^{2} (x^{2} + 6)^{3})

= 10 ((x^{2} + 6)^{4} + 8 x^{2} (x^{2} + 6)^{3})

x \to 2 - lim (x (x - 1))

\int \frac{1}{25 - x} d x

n = 1 \sum \infty (2 x)^{n}

\frac{\partial}{\partial x} (y^{2} - 3 x^{3})

d er i v a t i v e f (x) = - 5 x