If w=xy+z and x=cot, y=sint, z=t then find \(\frac { dw }{ dt } \)

Using linear approximation find \(\sqrt { 0.082 } \)

If w=x²+y² and x=u²-v^2,y=2uv then find \(\frac { \partial w }{ \complement u } and\frac { \partial w }{ \partial v } \)

Evaluate : \(\underset { \left( x,y,z \right) \rightarrow \left( -1,0,4 \right) }{ lim } \frac { { x }^{ 2 }-{ ze }^{ zy } }{ 6x+2y-2z } \)