Find the Differentiate

Question

R(t)=(t+e^t)(8-√t)

Answer 1

First, note that we can rewrite the original function as R(t)=(t+e^t)(8-t^(1/2)). Then, we could multiply these two binomials using FOIL, or we can go ahead and take the derivative of the function as is, using the product rule. Using the product rule and basic derivative rules, we get:

R'(t)=(t+e^t)(-(1/2)t^(-1/2))+(8-t^(1/2))(1+e^t)

or

R'(t)=(t+e^t)(-1/(2√t))+(8-√t)(1+e^t).

Hope this helps!