Scene 1

To find the derivative of  (x 3 -2x 2 +1) 5

Scene 2

Using ‘Chain Rule’ (function of a function)

Chain Rule       dy 	   dy       du 	 dx	  du	   dx

Note:  we let those terms in the bracket be ‘u’

From the question;    Let ,     		 y = (x 3 -2x 2 +1) 5   	 So that,  u = x 3 -2x 2 +1

Which implies as    y = (u) 5   as u =  x 3 -2x 2 +1  	    so that: 		 	 dy 			      du                	du 			     dx

By applying the formula   	                             	  dy 	   dy       du 	 dx	  du	  dx Implies as; 	  dy         	 dx 	  dy         	 dx

Since, ‘u’ = x 3 -2x 2 +1 	 Therefore; 	       dy 		        dx