Question

Suppose that the function f and g and their derivatives with respect to x have the following values at the given values of x. Find the derivative with respect to x of the given combination at the given value of x.

x I f(x) I g(x) I f'(x) I g'(x)
----------------------
3 I 1 I 4 I 6 I 7
4 I -3 I 3 I 5 I -4

√(g(x), x=3

Answer 1

\[\frac{d}{dx}\sqrt{g(x)}=\frac{g'(x)}{2\sqrt{g(x)}}\] so compute \[\frac{g'(3)}{2\sqrt{g(3)}}\] as you have all the numbers you need