derivative of (8x-2x^2cos(y))

Lösung

\frac{d}{d x} ((8 x - 2 x^{2}) cos (y))

cos (y) (8 - 4 x) - sin (y) \frac{d y}{d x} (8 x - 2 x^{2})

Schritte zur Lösung

\frac{d}{d x} ((8 x - 2 x^{2}) cos (y))

Wende die Produktregel an:

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

f = 8 x - 2 x^{2}, g = cos (y)

= \frac{d}{d x} (8 x - 2 x^{2}) cos (y) + \frac{d}{d x} (cos (y)) (8 x - 2 x^{2})

\frac{d}{d x} (8 x - 2 x^{2}) = 8 - 4 x

\frac{d}{d x} (cos (y)) = - sin (y) \frac{d y}{d x}

= (8 - 4 x) cos (y) + (- sin (y) \frac{d y}{d x}) (8 x - 2 x^{2})

Vereinfache

= cos (y) (8 - 4 x) - sin (y) \frac{d y}{d x} (8 x - 2 x^{2})

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

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

\frac{d}{d x} (x x)

\int 3 d x

x \to 0 - lim (e^{\frac{8}{x}})