Let $f(x_1,x_2,\ldots,x_n)$ be a differentiable, real-valued function and given $n$ real numbers $a_1,a_2,\ldots,a_n$, this application calculates the value of function $f$ at $x_i=a_i$, where $i=1,2,\ldots,n$, and the gradient vector of $f$: $\mathrm{gradient}(f) = \left(\frac{\partial f}{\partial x_1},\frac{\partial f}{\partial x_2},\ldots,\frac{\partial f}{\partial x_n}\right)$ The $n$ partial derivatives $\frac{\partial f}{\partial x_i}$ are calculated using automatic differentiation (AD) as described in Derivative Calculator but in this case AD is applied to functions of serveral variables.
The calculator required from users two inputs: $f(x_1,x_2,\ldots,x_n)$ and $a_1,a_2,\ldots,a_n$. The math expressions for both inputs are the same format as described in Derivative Calculator but in this calculator we use x1 for $x_1$, x2 for $x_2$, etc. The $n$ real numbers $a_1,\ldots,a_n$ must be separated by at least one space.