R1 eksempeloppgave 2015 vår LØSNING

Oppgave 1

a)

$f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$

b)

$g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$

c)

$h(x)=ln(x^3+1)\\h'(x)=(lnu)'\cdot \ (x^3+1)' \= \frac{1}{x^3+1}\cdot \ 3x^2 \=\frac{3x^2}{x^3+1}$