MATLAB: How to code a function of relative rates

differential equations

Hello, I have a function 
d = sqrt(x^2+y^2)
then
 d' = (x.x'+y.y')/sqrt(x^2+y^2)
I tried 2 ways:
1st I do :
syms f(x) f(y)
>> d = sqrt(f(x)^2+f(y)^2)
d =
(f(x)^2 + f(y)^2)^(1/2)
>> diff(d)
ans =
(f(x)*diff(f(x), x))/(f(x)^2 + f(y)^2)^(1/2)
2nd I do
>> diff(d,x,y)
ans =
-(f(x)*f(y)*diff(f(x), x)*diff(f(y), y))/(f(x)^2 + f(y)^2)^(3/2)
but both of the answer are not what I want .
Is there any code lead to the result
(f(x)*diff(f(x), x)+f(y)*diff(f(y), y))/(f(x)^2 + f(y)^2)^(1/2)
What function should i use ?
Thank you !!!

Best Answer

syms x y f(t)
d = sqrt(f(x)^2+f(y)^2)
d = 
simplify(diff(d,x) + diff(d,y))
ans = 
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