<p>It is a common claim, that automatic differentiation and symbolic differentiation are different. However, this is not true. Forward mode automatic differentiation and symbolic differentiation are in fact equivalent. Please see this <a href="https://arxiv.org/abs/1904.02990" rel="noreferrer">paper</a>.</p>

<p>In short, they both apply the chain rule from the input variables to the output variables of an expression graph. It is often said, that symbolic differentiation operates on mathematical expressions and automatic differentiation on computer programs. In the end, they are actually both represented as expression graphs.</p>

<p>On the other hand, automatic differentiation also provides more modes. For instance, when applying the chain rule from output variables to input variables then this is called reverse mode automatic differentiation.</p>
Difference between symbolic differentiation and automatic differentiation?
<p>I just cannot seem to understand the difference. For me it looks like both just go through an expression and apply the chain rule.. What am I missing?</p>