Question

Can someone please explain how you calculate df/dx? Thank you!

This is the function `f(x)=sqrt(1-(x^2+y^2)`

`(delf)/(delx)= -x/(sqrt(1-(x^2+y^2)`

Answer 1

Please see below.

Explanation:

When we use `(delf)/(delx)` (instead of `(df)/(dx)`) it means that

we are using partial differentiation i.e. differentiating w.r.t. `x`, but considering other variables (here `y`) as constant .

As `f(x)=sqrt(1-(x^2+y^2))` using chain rule

`(delf)/(delx)=(delf)/(del(1-(x^2+y^2)))xx(del(1-(x^2+y^2)))/(delx)`

Now `(delf)/(del(1-(x^2+y^2)))=1/(2sqrt(1-(x^2+y^2))`

and `(del(1-(x^2+y^2)))/(delx)=(del(1-x^2-y^2))/(delx)=-2x` as we have considered `-y^2` as constant

Hence `(delf)/(delx)=1/(2sqrt(1-(x^2+y^2)))xx2x`

= `x/sqrt(1-(x^2+y^2))`