Question

g(x)+sine g(x) = x^2

Find g'(0) using implicit differentiation.

Answer 1

It's a bit hard to understand the question, but I think you will have: \[g'(x) + \cos(g(x)) g'(x) = 2x\]

Factor out a g'(x): \[g'(x)[1+\cos(g(x))] = 2x\]

Answer 2

Finally, divide: \[g'(x) = \frac{ 2x }{ 1+\cos(g(x)) }\]
and plug in zero.

Answer 3

So it's kinda similar to the chain rule then.

Answer 4

Well, you did use chain rule. So yes. Unless you had\[\sin(x)g(x)\] in which case you would use product rule instead of chain rule.

Answer 5

yup, that makes sense. Thank you!