Hello! I'm trying to follow the mathematics done on this webpage http://www.nrbook.com/a/bookfpdf/f9-7.pdf It's on Globally Convergent Methods for Nonlinear Systems of Equations. I can understand it up to this point:

The author has the following equation: g(\lambda) \equiv f(xold+\lambda p) equation 9.7.8 on the pdf and then he goes to this line g'(\lambda) = \nabla f \cdot P equation 9.7.9.

The problem is I don't know how he went between the two equations. I'm sure he differentiated with respect to \lambda but I don't know how he worked out the right hand side of equation 9.7.9.

I would be grateful if anyone could help me with this.