Find   by using the Chain Rule. Express your final answer in terms of t.

Solve the problem.Find the equation for the tangent plane to the surface x2 + 6xyz + y2 = -4z2  at the point (-1, -1, -1).

Find the absolute maxima and minima of the function on the given domain. f(x, y) = 2×2 + 6y2  on the disk bounded by the circle x2 + y2 = 9 

Solve the problem.Find the derivative of the function at the point (-4, 4, -4) in the direction in which the function increases most rapidly.

Find the limit.  

Give an appropriate answer.Express

Find all the first order partial derivatives for the following function.f(x ,y, z) = (sin xy)(cos yz2)

Use implicit differentiation to find the specified derivative at the given point.Find

Find all the first order partial derivatives for the following function.f(x, y, z) = cos x sin2 yz

Some scientists think that the Yellowstone Supervolcano could cause a future disaster because: