Let w(x, y, z) Calculate dx dt dy dt dz dt || dw dt || || dw dt 4t3 3t² 9 = 4xy arcsin (z) where x by first finding dx dy dt' dt Hint: Recall the chain rule: dw dt || & ( dz dt ४ -1 Now use the chain rule to calculate the following (please enter arcsin instead of sin whenever appropriate): : t¹, y = t³, z = = B and using the chain rule. dw dx 9t. əx dt + δω dy მყ dt dw дz dz dt Let w(x, y, z) = x² + y² + z² where x = sin (9t), y = cos(— 9t), z = e¯³t. 3t dw Calculate by first finding dt dx dt || dz dt dy = 9 sin(-9t) dt 9 cos (9t) || -3e-3t dx dy " dt dt Hint: Recall the chain rule: dw & Now use the chain rule to calculate the following: dw dt dt dz dt and using the chain rule. = (ow θω dx dt dw მყ dy dt dw дz dz dt Let z(x, y) dx dt dy dt = || dz dt Calculate by first finding & 9t8 8e* sin(y) where x = = 3πT dx dy dt dt Hint: Recall the chain rule: to & y dz dt = = Now use the chain rule to calculate the following: dz dt 3πt. and using the chain rule. dx dy (20) - (0) + dt dt