derivative of x(4x-5^3)

Lösung

\frac{d}{d x} (x (4 x - 5)^{3})

(4 x - 5)^{3} + 12 x (4 x - 5)^{2}

Schritte zur Lösung

\frac{d}{d x} (x (4 x - 5)^{3})

Wende die Produktregel an:

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

f = x, g = (4 x - 5)^{3}

= \frac{d x}{d x} (4 x - 5)^{3} + \frac{d}{d x} ((4 x - 5)^{3}) x

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

\frac{d}{d x} ((4 x - 5)^{3}) = 12 (4 x - 5)^{2}

= 1 \cdot (4 x - 5)^{3} + 12 (4 x - 5)^{2} x

Vereinfache

= (4 x - 5)^{3} + 12 x (4 x - 5)^{2}

\int_{0}^{2} 4 x e^{x} d x

x \to 1 lim (\frac{4 x + 3}{2 x + 1})

n = 1 \sum \infty 4 \cdot (\frac{4}{7})^{n}

\int (\frac{x ( x - 8 )}{x + 1})^{2} d x

d er i v a t i v e f (x) = 5 x (sin (x) + cos (x))