Question

Use the product rule to calculate the derivative.
dh
dx
x = 4 ,

h (x) = (x^(-1/2) + 7x)(9 - x^-1)

very weird.. i know how to do it, i used product rule and got an answer in decimal but the website is not accepting it. Can any one help me?...

Answer 1

Let's multiply it out and not use the product rule. The answer should be the same.

h(x) = 9x^(-1/2) -x^(-3/2) +63x -7
dh/dx = -(9/2)x^(-3/2) +(3/2)x^(-5/2) + 63

dh/dx @ x=4 = (-9/2)(1/8) +(3/2)(1/32)+63
= -9/16 +3/64 +63