I am looking for help on page 128 equation (14) from zee's book Einstein Gravity. A lot of you may not have the book. I have a phd and cannot see it, feel really really stupid. How did he get rid of the square roots. I know that he used the definition of the derivative from basic calculus with out the delta x on the bottom. In the first square root he varied the action so that L moves to the bottom. You need the second g so the taylor series starts off with a derivative. How does the square root go away when the second part is not varied. I will use different symbols from the book, but they are only dummy variables so I can change them. Plus it makes it easier to write out the equation. ∂gκμδX = gκμ(X(λ) + δX(λ)) - gκμ(X(λ)) so you need the second term. Please remember κ and μ are just dummy variables so I am free to choose them, as long as I carry them through. The κ and μ are indices.