I have a problem from thomas' calculus. the topic is Tangent planes and diffrentials. The problem is as follows: the celcus temparature in a region in space is given by T(x,y,z)= 2*x^2-xyz; a particle is moving in the region and it's position at time t is given by x=2*t^t ; y=3*t; z=-t^2, where time is measured in seconds and distance in meters. then how fast is the temparature experienced by the particle changing in degrees per meter when the particle is at the point P(8,6,-4)?
ther was another problem just above this problem. there says ; suppose that the celcius temparature at the point (x,y) in the xy-plane is T(x,y)=x-sin(2y) and the distance is in meters. a particle is moving clockwise aroun the circle of radius 1m centered at te origin at the constant rate of 2m/sec.
and it asks : how fast is the temparature experienced by the particle changing in degrees per meter when the particle is at the point
I have sold the second question as folows. I find the direction of the particle when iti s at the poin P. then I took he directional derivative at this point. However, in the first question how can ı find the direction o the particle?