The derivative of f( x) with respect to g( x) at x = 4 , given that f' ( 1 2 ) = 3 and g'( 2 ) = 1 is.....

Step-by-step solution

Let u = f( x) and v = g( x) du dx = f'( x) x dv dx = g'( x) x x du dv = du dx dv dx = f'( x) x g'( x) x x At x = 4 : du dv = f' ( 1 2 ) 1 2 g'( 2 ) 2 1 Substituting f' ( 1 2 ) = 3 and g'( 2 ) = 1 : du dv = 3 1 2 1 2 = 3 2 Answer: 3 2