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,…,x_n], a vector of the variable names.
• derive(expr,[x₁,…,x_n]) returns the gradient of expr; namely, the vector of partial derivatives of expr with respect to x₁, …, x_n.

  For instance, in dimension n=3, with variables [x,y,z]:

  ▸ grad

  (F)=

  ⎡ ⎢ ⎢ ⎣

  ∂ F ∂ x

  ,

  ∂ F ∂ y

  ,

  ∂ F ∂ z

  ⎤ ⎥ ⎥ ⎦

  .

Example

Find the gradient of F(x,y,z)=2x²y−xz³.

or:

or:

To find the critical points of F(x,y,z)=2x²y−xz³: