Help on using the chain rule

You are asked to determine the Partial Derivative wrt y.
So, you differentiate treating x as a constant.

Rewrite the function using fractional exponents.
Then differentiate using the chain rule.
——————————————————————————————————————
    ∂  1/√(x²+y²)
   —————–
           ∂y


    ∂  (x²+y²)⁻¹ʹ²
= —————–
          ∂y


                            ∂ (x²+y²)
=  -½(x²+y²)⁻³ʹ² • —————     ← Now, differentiate (x²+y²) treating x as a constant
                                ∂y


=  -½(x²+y²)⁻³ʹ² • (0 + 2y)

=  -½(x²+y²)⁻³ʹ² • (2y)

= -y(x²+y²)⁻³ʹ²

= -y / (x²+y²)³ʹ²                ← ANSWER ... D


Have a good one!
——————————————————————————————————————

You are asked to find the partial derivative with respect to y
of the function f(x,y)=1/sqrt(x^2+y^2)
so the first step is to rewrite the function as(x^2+y^2)^(-1/2)
Now we use the power rule in conjunction with the chain rule
-1/2(x^2+y^2)^(-3/2)*2y=
-2y/2(x^2+y^2)^3/2=
-y/(x^2+y^2)^(3/2)