derivative of 20x(2x^2+7^4)

Lösung

\frac{d}{d x} (20 x (2 x^{2} + 7)^{4})

20 ((2 x^{2} + 7)^{4} + 16 x^{2} (2 x^{2} + 7)^{3})

Schritte zur Lösung

\frac{d}{d x} (20 x (2 x^{2} + 7)^{4})

Entferne die Konstante:

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

= 20 \frac{d}{d x} (x (2 x^{2} + 7)^{4})

Wende die Produktregel an:

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

f = x, g = (2 x^{2} + 7)^{4}

= 20 (\frac{d x}{d x} (2 x^{2} + 7)^{4} + \frac{d}{d x} ((2 x^{2} + 7)^{4}) x)

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

\frac{d}{d x} ((2 x^{2} + 7)^{4}) = 16 x (2 x^{2} + 7)^{3}

= 20 (1 \cdot (2 x^{2} + 7)^{4} + 16 x (2 x^{2} + 7)^{3} x)

Vereinfache

20 (1 \cdot (2 x^{2} + 7)^{4} + 16 x (2 x^{2} + 7)^{3} x) : 20 ((2 x^{2} + 7)^{4} + 16 x^{2} (2 x^{2} + 7)^{3})

= 20 ((2 x^{2} + 7)^{4} + 16 x^{2} (2 x^{2} + 7)^{3})

d er i v a t i v e 2 + 6 x^{2} - 2 x^{3}

\int - 3 x^{2} - 2 d x

\frac{\partial}{\partial x} (a x^{2} + b y^{2})

\frac{d}{d x} (\frac{x}{x ^{2} + 81})

d er i v a t i v e f (x) = 3 x + \frac{8}{x ^{3}}