In the end, what I would like to have is this in Latex Code
\frac{\partial \Theta(U(x),x)}{\partial U(x)} \frac{U(x))}{\partial x} +
\frac{\partial \Theta(U(x),x)}{\partial x}
and I want to obtain that just from the expression
# Declaration
x = symbols('x')
U, Theta = symbols('U Theta', cls=Function)
# Function to derive
obj_function = Theta(U(x),x)
and derive that w.r.t. "x" which is what mathematically makes sense to me.
On Friday, May 1, 2015 at 1:19:19 PM UTC-5, Isuru Fernando wrote:
>
> Hi,
>
> I'm not sure how to do the substitution, but why do you expect
> obj_function.diff(x) to be
> Derivative(Theta(U(x), x), x) + Derivative(U(x), x)* Derivative(Theta(U(x),
> x), U(x)) ?
>
> I think the answer you are getting from sympy is not correct.
> obj_function.diff(x) should be the same as Derivative(Theta(U(x), x), x),
> but that is not what sympy is giving.
> See, https://github.com/sympy/sympy/issues/8510
>
> CSymPy is giving,
> Derivative(U(x), x)*Subs(Derivative(Theta(_x, x), _x), (_x), (U(x))) +
> Subs(Derivative(Theta(U(x), _x), _x), (_x), (x))
> which I think should be the correct answer.
>
> Here what Subs(Derivative(Theta(U(x), _x), _x), (_x), (x)) means is
> partial differentiate Theta with respect to the second variable and replace
> the first variable with U(x) and the second with x.
> (D[2](Theta)(U(x), x) is the equivalent in Maple syntax or Derivative[0,
> 1][Theta][U[x], x] in Mathematica syntax)
>
> Isuru Fernando
>
>
> On Fri, May 1, 2015 at 8:16 PM, Miguel Angel Salazar de Troya <
> [email protected] <javascript:>> wrote:
>
>> Hello
>>
>> I have this derivative of a function that has an argument which is also a
>> function
>>
>> # Declaration
>> x = symbols('x')
>> U, Theta = symbols('U Theta', cls=Function)
>>
>> # Function to derive
>> obj_function = Theta(U(x),x)
>>
>> # Derivative
>> gradient_obj_function = obj_function.diff(x)
>>
>> And this is the output I obtain
>>
>> Derivative(Theta(U(x), x), x) + Derivative(U(x),
>> x)*Subs(Derivative(Theta(_xi_1, x), _xi_1), (_xi_1,), (U(x),))
>>
>> How can I replace Subs(Derivative(Theta(_xi_1, x), _xi_1), (_xi_1,),
>> (U(x),)) with Derivative(Theta(U(x), x), U(x)) ?
>> I found this post,
>> https://groups.google.com/forum/#!searchin/sympy/"chain$20rule"/sympy/OfF5PklJtmY/t1FPWt3n8xIJ,
>>
>> but it was not clear to me how this has to be done.
>>
>> Thanks
>> Miguel
>>
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