RE Finding derivatives from a table? Find the values of the following derivatives using the table. a.? d [f(X)+2g(x)] b .?d [x f(x] dx x=3 dx g(x) x=1 c.? d[f(g(x )] x=3 dx

Solution Step 1: Given x 1 3 5 7 9 f(x) 3 1 9 7 5 f’(x) 7 9 5 1 3 g(x) 9 7 5 3 1 g’(X 5 9 3 1 7 ) Step 2: (a)We have to determine d [f(X) + 2g(x)] dx x=3 d [f(x) + 2g(x)] =[f x) + 2g()] dx x=3 x=3 =f 3) + 2g(3 =9+2(9) (from table f () = 9, g(3) 9) =27 Step 3: (b) d[ x f(]) dx g(x) x=1 We know that d dv du dx(uv )=u dx+ v dx v u dv d ( ) = dx2 dx dx v v