R1 2011 vår LØSNING

a)

<tex>O(x)= \frac{500}{x} + 8x^2 \\ O(x) = 500x^{-1} + 8x^2 \\ O'(x) = -500x^{-2}+ 16x = \frac{-500}{x^2} + 16x = \frac{-500 +16x^3}{x^2}</tex>

b)

1)

<tex>f(x)= 3ln(2x) \\ f'(x) = 3 \cdot \frac{1}{(2x)}\cdot 2 = \frac {6}{2x} = \frac 3x</tex>

2)

<tex>g(x) = 3x \cdot e^{x^2} \\ g'(x) = 3e^{x^2}+3x \cdot 2x \cdot e^{x^2} = (3+6x^2)e^{x^2}</tex>

c)

d)

e)

f) g) h)