Page 2.49 by xmung on June 12, 2005 at 12:01 am Chapter: The Great Leap ForwardLocation: Magellan Island

Let’s see.

g(x) = sqrt(x) * f(x)

g'(x) = 1/sqrt(x) * f(x) + f'(x) sqrt(x)

g'(4) = 1/sqrt(4) * f(4) + f'(x) sqrt(4)

g'(4) = 1/2 * 3 + 5 * 2

g'(4) = 0.75 + 10

g'(4) = 10.75

Way to go Fatima.

Oh wait, I goofed the square root rule and some of the simplifying. I think I got suckered by a confirmation bias.

sqrt(x) = x^(1/2)

d sqrt(x)/dx = (1/2) x^(-1/2) = 1/(2sqrt(x))

Therefore,

g'(x) = f(x)/(2sqrt(x)) + f(x) sqrt(x)

g'(4) = f(4)/(2sqrt(4)) + f(4) sqrt(4)

g'(4) = 3/(2*2) + 5 * 2

g'(4) = 3/4 + 10

g'(4) = 10.75