Question

suppose that (g(x))^2+6x=x^2g(x)+17 and g(2) =5 find g'(2)

Answer 1

Have you considered calculating the derivative, g'(x)? It's a nice implicit exercise.

Answer 2

Left side... 2(g(x))g'(x) + 6
You do the right side.

Answer 3

is this right

Answer 4

2xg(x)+d/dx

Answer 5

d/dx of what?

Answer 6

You need to apply the product rule on that x^2*g(x) part

Answer 7

okay so is it 2(g(x))g'(x)+6=3g(x)^2

Answer 8

now what?

Answer 9

Right side x^2g(x)+17

x^2g'(x) + 2xg(x)

Where did 3g(x)^2 come from?