Question

If z=e^(xy^2),x=tcost,y=tsint,compute dz/dt at t=π/2?

Answer 1

`- (pi/2)^3`

Explanation:

`z=e^(xy^2)`

`dz/dt= (del z)/(delx) dx/dt + (delz)/(dely) dy/dt`

`=e^(xy^2) (y^2) (cost -t sint) +e^(xy^2) (x) (2y dy/dt) ( sint +t cost)`

`=e^(xy^2) (y^2) (cost - tsin t)+e^(xy^2) 2xy (sint +tcost)^2`

At `t=pi/2, cost =0, sint =1, x=0 and y= pi/2`

Therefore `dz/dt =(pi/2)^2 (-pi/2)= -(pi/2)^3`