Gradient Calculator

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.

Input Data

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.

Gradient Calculator

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