log ( ) y ( ) yx y − ( ) x . If f x y e xy ( , ) = , then ∂ ∂∂ f x y is equal to ( ) xye xy ( ) ( + xy e xy ( ) ( + y e xy ( ) ( + x e xy . If we measure the side of a cube to be cm with an error of . cm, then the error in our calculation of the volume is ( ) .
cu.cm ( ) . cu.cm ( ) cu.cm ( ) . cu.cm . The change in the surface area S = of a cube when the edge length varies from x to + is ( ) x ( ) x dx ( ) x dx ( ) x .
The approximate change in the volume V of a cube of side x metres caused by increasing the side by % is ( ) . xdx m ( ) xm ( ) x m ( ) x m . If g x y x t e t , ( ) and y t , then dg dt is equal to ( ) e t + cos sin ( ) e t − cos sin ( ) e t + cos sin ( ) e t − cos sin and - - . If f x ( ) = + , then its differential is given by ( ) ( ) ( ) ( ) − .
If u x y ( , ) = , then ∂ x ( , is equal to ( ) − ( ) − ( ) − ( ) . Linear approximation for g x at x = π is ( ) x + π ( ) −+ ( ) x − π ( ) −− . If w x y z z z z ( , , ) , then ∂ ∂ + ∂ ∂ + ∂ w w