Both gradient and total derivative are a collection or combination of the partial derivatives with respect to each input variable?
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$\begingroup$The total derivative of a map from $\mathbb R^n$ to $\mathbb R^m$ is the $m\times n$ matrix of first partial derivatives. The gradient is defined on functions from $\mathbb R^n$ to $\mathbb R$. It is the $1\times n $ vector of partial derivatives. So you could say that the total derivative consists in the matrix whose rows are the gradients of the coordinate functions. (Hope I got my $m$'s and $n$'s in the right places!)
$\endgroup$ 2 $\begingroup$Given a function $f : \mathbb R^n \rightarrow \mathbb R^m$, the total derivative is the matrix of partial derivatives, and the gradient is another name for the total derivative in the case $m=1$. if $m > 1$, there is no gradient.
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