Let f , g and h are differentiable functions. If f 0 = 1 ; g 0 = 2 ; h 0 = 3 and the derivatives of their pair wise products at x = 0 are fg ' 0 = 6 ; gh ' 0 = 4 and hf ' 0 = 5 , then the value of fgh ' 0 is

Step-by-step solution

Let, y = fgh dy dx = f ' gh + fg ' h + fgh ' = 1 2 2 f ' gh + 2 fg ' h + 2 fgh ' = 1 2 h f ' g + g ' f + g f ' h + fh ' + f g ' h + gh ' = 1 2 h . fg ' + g . fh ' + f . gh ' fgh ' 0 = 1 2 h 0 fg ' 0 + g 0 fh ' 0 + f 0 gh ' 0 = 1 2 3 × 6 + 2 × 5 + 1 × 4 = 1 2 1 8 + 1 0 + 4 = 3 2 2 = 1 6