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

Question

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

Answer 1

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

 

You won't really need the product rule for this one.  You can expand h(s) using FOIL.  Then derive h(s) using the derivative of sums.

 

h(s) = 7s^-1/2 - s^-3/2 + 14s - 2

 

 

Now derive h(s) using the power rule.

Answer 2

Use the product rule.  Let f(s) = s^(-1/2) + 2s and g(s) = 7-s^-1

Then the derivative of h(s) = f(s)*g'(s) + f'(s)*g(s)

 

Use polynomial derivative rules to find the derivative of f(s) and g(s)

f'(s) = (-1/2)s^(-3/2) + 2

g'(s) = s^(-2)

 

Now substitute into the product rule (I don't want to type it all in case I mis-type an exponent).

Distribute or use FOIL with the parentheses if you teacher prefers the answer in expanded form (there may be like terms that you can combine).

 

I am available for tutoring sessions online if you have additional questions (p.s. I love Calculus).