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Taylor Expansion (multivariate)

Hi, I need some help understanding the taylor expansion of a function $\displaystyle g_0(\phi,c,T)$. I'm particularly confused with the 3rd term on the RHS. Why is there a partial derivative there? When I expand it, I get the same as whats in the image but no multiplication with partial derivatives.

Thanks

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Re: Taylor Expansion (multivariate)

Thanks for replying ojones. Turns out the partial derivative multiplying the 3rd term and other terms were a typo. That's odd since this typo was present in multiple papers.