Let

z(x,y)=xy

where

x=rcos(8\\\\theta )&y=rsin(5\\\\theta )

.\ Calculate

(delz)/(delr)&(delz)/(del\\\\theta )

by first finding

(delx)/(delr),(dely)/(delr),(delx)/(del\\\\theta )&(dely)/(del\\\\theta )

and using the chain rule.\ Note: To produce the

\\\\theta

symbol, type the word "theta".\

(delz)/(delr)=\ (delz)/(del\\\\theta )=

\ Hint: Recall the chain rule: For

z(x(s,t),y(s,t))

, we have

(delz)/(delt)=((delz)/(delx)*(delx)/(delt))+((delz)/(dely)*(dely)/(delt))

Let z(x,y)=xy where x=rcos(8)&y=rsin(5). Calculate rz&z by first finding rx,ry,x&y and using the chain rule. Note: To produce the symbol, type the word "theta". rz=z= Hint: Recall the chain rule: For z(x(s,t),y(s,t)), we have tz=(xztx)+(yzty) Let z(x,y)=xy where x=rcos(8)&y=rsin(5). Calculate rz&z by first finding rx,ry,x&y and using the chain rule. Note: To produce the symbol, type the word "theta". rz=z= Hint: Recall the chain rule: For z(x(s,t),y(s,t)), we have tz=(xztx)+(yzty)