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2.50.1  Gradient : derive deriver diff grad

derive (or diff or grad) takes two arguments : an expression F of n real variables and a vector of these variable names.
derive returns the gradient of F, where the gradient is the vector of all partial derivatives, for exmple in dimension n=3


grad
 
(F)= [
∂ F
∂ x
,
∂ F
∂ y
,
∂ F
∂ z

Example
Find the gradient of F(x,y,z)=2x2yxz3.
Input :

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])

Output :

[2*2*x*y-z^3,2*x^2,-(x*3*z^2)]

Output after simplification with normal(ans()) :

[4*x*y-z^3,2*x^2,-(3*x*z^2)]

To find the critical points of F(x,y,z)=2x2yxz3, input :

solve(derive(2*x^2*y-x*z^3,[x,y,z]),[x,y,z])

Output :

[[0,y,0]]

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