 
 
 
13.7.1  Gradient
The derive
command finds partial derivatives of a multivariable expression.
diff and grad
can be used synonymously for derive here.
- 
derive takes two arguments:
- 
expr, an expression involving n real variables.
- [x1,…,xn], a vector of the variable names.
 
- derive(expr,[x1,…,xn])
returns the gradient of expr; namely, the vector of partial
derivatives of
expr with respect to x1, …, xn.For instance, in dimension n=3, with variables [x,y,z]:
 
Example
Find the gradient of F(x,y,z)=2x2y−xz3.
| derive(2*x^2*y-x*z^3,[x,y,z]) | 
or:
| diff(2*x^2*y-x*z^3,[x,y,z]) | 
or:
| grad(2*x^2*y-x*z^3,[x,y,z]) | 
|  | | |  | ⎡ ⎣
 | 2· 2 x y−z3,2 x2,−3 x z2 | ⎤ ⎦
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
|  | | |  | ⎡ ⎣
 | 4 x y−z3,2 x2,−3 x z2 | ⎤ ⎦
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
To find the critical points of F(x,y,z)=2x2y−xz3:
| solve(derive(2*x^2*y-x*z^3,[x,y,z]),[x,y,z]) | 
 
 
