Question

Suppose [g(x)]^2+12x=x^2*g(x) and g(4)=12. Find g'(4)?

Answer 1

do you know chain rule ?

Answer 2

I know what the chain rule is but I don't know how to apply it this one

Answer 3

ok,
d/dx [g (x)]^2 = 2 g(x) d/dx [g(x)]

does this make sense ?

Answer 4

It makes sense

Answer 5

good,
and can you differentiate x^2*g(x)
using product rule ?

Answer 6

2x*g(x)+g'(x)*x^2 right?

Answer 7

correct! :)

Answer 8

so, what do we have now ?
2 g(x) g'(x) +12 = 2x*g(x)+g'(x)*x^2
right ?
with me till here ?

Answer 9

Yeah, I got it

Answer 10

now to get g'(4) , just plug in x=4 !
replace x by 4 wherever you see it there ..

Answer 11

could you find g'(4) ?