Temperature (in degrees Celsius) at the point (x, y, z) at time t is given by the formula T (x, y, z, t) = x^2 + 2y^2 + x*cos (t). The thermometer travels around space under the parametric curve r (t) = (3t, t2,2t) where distances are given in meters and time unit is seconds.
( A) What is the change in temperature in ◦C / s which the thermometer detects at time t?
I'm not sure how I can solve this, I should find dT/dt right?

Question

Temperature (in degrees Celsius) at the point (x, y, z) at time t is given by the formula T (x, y, z, t) = x^2 + 2y^2 + x*cos (t). The thermometer travels around space under the parametric curve r (t) = (3t, t2,2t) where distances are given in meters and time unit is seconds. 
( A) What is the change in temperature in ◦C / s which the thermometer detects at time t? 
I'm not sure how I can solve this, I should find dT/dt right?

irishboy123 · Answer

yeah, just plug the params into T