Use product rule to calculate derivative

Question

h(s)=(s^-1/2+2s)(7s-s^-1)

Answer 1

If h(s) = u • v then h'(s) = u'v + uv' (that's the product rule)

Let u = (s^-1/2+2s) and v = (7s-s^-1)

Take the derivative of each of those using the power rule

u' = -1/2s^-3/2 + 2 and v' = 7 - (-s^-2)

So h'(s) = [-1/2s^-3/2 + 2][7s - s^-1] + [s^-1/2 + 2s][7 - (-s^-2)]

That's the easy part. If your teacher let's you leave the answer like that, do it. If not, simplify using your algebra skills. If simplifies to h'(s) = 28s +7/2s^-1/2 + 3/2s^-5/2