SOLUTION: An equation is given: r^2 + 2st^(1/2) = rt. A) Find ds/dr B) Find dr/dt C) Find dt/ds D) Find dr/ds

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: An equation is given: r^2 + 2st^(1/2) = rt. A) Find ds/dr B) Find dr/dt C) Find dt/ds D) Find dr/ds      Log On


   

Question 1027708: An equation is given: r^2 + 2st^(1/2) = rt.
A) Find ds/dr
B) Find dr/dt
C) Find dt/ds
D) Find dr/ds
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
r%5E2+%2B+2st%5E%281%2F2%29+=+rt is an implicit function of three variables.
(A) The partial derivative ds/dr is 2r+%2B+2%28ds%2Fdr%29t%5E%281%2F2%29+=+t
==> ds%2Fdr+=+%28t+-+2r%29%2F+%282t%5E%281%2F2%29%29.
(B) The partial derivative dr/dt is 2r%28dr%2Fdt%29+%2B+2s%281%2F2%29%281%2Ft%5E%281%2F2%29%29+=+%28dr%2Fdt%29t+%2B+r
==> 2r%28dr%2Fdt%29+%2B+s%2Ft%5E%281%2F2%29+=+%28dr%2Fdt%29t+%2B+r
%282r+-+t%29%28dr%2Fdt%29+=+r+-+s%2Ft%5E%281%2F2%29
dr%2Fdt+=+%28r+-+s%2Ft%5E%281%2F2%29%29%2F%282r+-+t%29
I leave parts (C) and (D) for you to practice on.