ACTIVITY 2 : Keep Practicing ! DERIVATIVE OF A FUNCTION AT A NUMBER Let f be a function and x = c is a value in its domain. The derivative of f with respect to x evaluated at x = c is denoted by f' ( c ). We first find the derivative of the function using the differentiation rules, then we substitute the value of c. Example : Ifg ( x ) = In (x ) ; solve for g' ( 2) Solution : g' ( x ) = 1 . . X g' (2 ) = = Now it's your turn ! Find the indicated derivative : 1) f ( x ) = x5 - 2x2 + = ; find f' (-1 ) 2) y = 2x2 ; solve for y ' ( 4 ) 3) X = 3t3 - 212 determine if t = 0 2t2ACTIVITY 1 : Practice ! Find the derivative as indicated : 1) y = 3 cos x + 2 sin x ; find y' 3) f( x ) = x2 tan x ; find 2) f ( t ) = t sin t ; find f' ( ") 4) x = =3t ; find dx cost ACTIVITY 2 : Keep Practicing ! Differentiate the following inverse trigonometric functions : 1) y = -2 sin-1 x 3) g ( u ) = - csc lu + sec 1 u 2) s ( t ) = - cos-1 t 4) f ( w ) = _ tan w 3 ACTIVITY 1: Practice ! Apply differentiation rules in finding the derivative of the given functions. Express your final answers in simplest form. 1) y =; x 5 3) g ( x ) = ( 2x )3 2) f ( x ) = 4) x = 1+ 43 3