# Multivariable calculus, gradient, directional derivatives

1. Apr 24, 2012

### miglo

1. The problem statement, all variables and given/known data
the Celsius temperature in a region in space is given by T(x,y,z)=2x^2-xyz. a particle is moving in this region and its position at time t is given by x=2t^2, y=3t, z=-t^2, where time is measured in seconds and distance in meters
a) how fast is the temperature experienced by the particle changing in degrees Celsius per meter when the particle is at P(8,6.-4)?
b) how fast is the temperature experienced by the particle changing in degress celsius per second at P?

2. Relevant equations
directional derivatives?

3. The attempt at a solution
ill admit i havent actually attempted anything because im not sure how to start
this problem comes from a practice exam under the section on tangent planes and differentials but i dont see how that would be helpful
to me it seems like more of a directional derivative problem but im not really sure
can someone please show me how to start this problem?