Answer
a) 13
b) -7
c) $\frac{7}{25}$
d) 20
Work Step by Step
a) $\frac{d}{dx}uv =uv' +vu' = u(0)v'(0) +v(0)u'(0) = 5(2) -1(-3) = 13$
b) $\frac{d}{dx}(\frac{u}{v}) = \frac{v(0)u'(0) - u(0)v'(0)}{v(0)^{2}} = \frac{3-10}{1} = -7$
c) $\frac{d}{dx}(\frac{v}{u}) = \frac{u(0)v'(0) - v(0)u'(0)}{u(0)^{2}} = \frac{7}{25}$
d) $ \frac{d}{dx}(7v-2u) = 7v'(0)- 2u'(0)= 7(2)-2(-3)= 14+6= 20$
