Use the Product Rule to calculate the derivative for the function ℎ(𝑠)=(𝑠^−1/2 +5𝑠)(7−𝑠^−1) at 𝑠=4.

Question

dh/ds |𝑠=4 =

Answer 1

Product Rule:

The derivative of a product of two functions is the first function times the derivative of the second function, plus the second function times the derivative of the first function.

dh/ds = [s^(-1/2) + 5s][s^(-2)] + [7 - s^(-1)][(-1/2)s^(-3/2) + 5]

At s = 4, dh/ds = 2215/64