How to code a function of relative rates

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 !!!

[Matt J]

but both of the answer are not what I want .

Is it supposed to be clear what answer you do want? The results you've presented seem correct to me.

[abc def]

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)

Answer 1

[Walter Roberson]

syms x y f(t)
d = sqrt(f(x)^2+f(y)^2)

d = 

simplify(diff(d,x) + diff(d,y))

ans = 

[abc def]

if i have:

d'=(f(x)*diff(f(x), x)+f(y)*diff(f(y), y))/(f(x)^2 + f(y)^2)^(1/2)

d'=-7sqrt(2)

f(x) = f(y) = 4sqrt(2)

diff(f(x), x) = -8

then can i solve diff(f(y), y) ? Like this

in the image the final line y'=-6 , i type it wrong