How Can dv/dx Be Determined to Solve for dv/dt?

wololo · Nov 3, 2015

Homework Statement

Typed calculus problem: x(s,t) = -4s^2 - 2t^2, y(1,1) = 1, dy/dt(1,1) = -2, u = xy, dv/dy(-6,1) = 4, f = u(x,y), g = v(x,y), with df/ds(1,1) = -32, df/dt(1,1) = 8, dg/ds(1,1) = -16; asks for dg/dt(1,1).

Homework Equations

Chain rule, partial derivation

The Attempt at a Solution

dv/dt=dv/dx*dx/dt+dv/dy*dy/dt
dx/dt=-4t -> evaluate at (1,1) =-4
dv/dt=-4dv/dx+4(-2)
dv/dt=-4dv/dx-8

How can I find the missing dv/dx in order to get a value for dv/dt? Thanks!

mfb · Nov 4, 2015

Did you expand the other derivatives to see if you get additional constraints from them?

How Can dv/dx Be Determined to Solve for dv/dt?

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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