Answer:
a)-50
b)-15/32
c) 6/5
d) 57
Explanation:
a)
[tex]\frac{d}{dx}(uv)[/tex]
[tex]u(x)v'(x)+u'(x)v(x)[/tex]
Evaluate this at [tex]x=0[/tex] we get:
[tex]u(0)v'(0)+u'(0)v(0)[/tex]
[tex]5(-2)+-5(8)[/tex]
[tex]-10+-40[/tex]
[tex]-50[/tex]
b)
[tex]\frac{d}{dx}(\frac{u}{v})[/tex]
[tex]\frac{u'(x)v(x)-u(x)v'(x)}{(v(x))^2}[/tex]
Evaluate this at [tex]x=0[/tex] we get:
[tex]\frac{u'(0)v(0)-u(0)v'(0)}{(v(0))^2}[/tex]
[tex]\frac{-5(8)-5(-2)}{(8)^2}[/tex]
[tex]\frac[-40+10}{64}[/tex]
[tex]\frac{-30}{64}[/tex]
[tex]\frac{-15}{32}[/tex]
c)
[tex]\frac{d}{dx}(\frac{v}{u})[/tex]
[tex]\frac{v'(x)u(x)-v(x)u'(x)}{(u(x))^2}[/tex]
Evaluate this at [tex]x=0[/tex] we get:
[tex]\frac{v'(0)u(0)-v(0)u'(0)}{(u(0))^2}[/tex]
[tex]\frac{-2(5)-8(-5)}{(5)^2}[/tex]
[tex]\frac{-10+40}{25}[/tex]
[tex]\frac{30}{25}[/tex]
[tex]\frac{6}{5}[/tex]
d)
[tex]\frac{d}{dx}(-6v-9u)[/tex]
[tex]-6v'(x)-9u'(x)[/tex]
Evaluate this at [tex]x=0[/tex]:
[tex]-6v'(0)-9u'(0)[/tex]
[tex]-6(-2)-9(-5)[/tex]
[tex]12+45[/tex]
[tex]57[/tex]
