If w=sqrt(x^2+y^2) x=ln(rs+tu) y=t/u(cos(rs))... find dw/dt, dw/ds, dw/dr, dw/du.I'm confused on what the difference between dw/dt & dw/ds is and what exactly is dw? Thanks!

Expert Answers
rcmath eNotes educator| Certified Educator

We are going to assume that t,s,r, and u are independant from each other.

For sake of simplicity, I am going to use the ' symbol first, then differentiate appropriately.

`w=sqrt(x^2+y^2) =>`





If we differentiate with respect to t, the other 3 variables are going to be treated like constants, so







To differentiate with respect to u, you treat t, r, and s like constant and you differentiate appropriately.