Who is responsible for coming up with the gradient and why did they do so? In which work was it first described?

I have Googled this extensively, to no avail, and Boyer's History of Calculus does not appear to contain the answer to this.

The vector differential operator, now written $$\nabla$$ and called nabla or del, was introduced by William Rowan Hamilton (1805-1865). Hamilton wrote the operator as a [90°] rotated nabla and it was P.G.Tait who established $$\nabla$$ as the conventional symbol; see his An Elementary Treatise on Quaternions (1867). Tait was also responsible for establishing the term nabla.
The vector sum which is the resultant rate of increase of $$V$$ is denoted by $$\nabla V$$.
$$\nabla V$$ represents a directed rate of change of $$V$$ - a directed or vector derivative of $$V$$, so to speak. For this reason $$\nabla V$$ will be called the derivative of $$V$$; and $$V$$, the primitive of $$\nabla V$$. The terms gradient and slope of $$V$$ are also used for $$\nabla V$$.