Help with C please

16) Find the first derivative of f(x) = 5 ( 7 x 2 + 1 ) 3 5 points a ) by using quotient rule. Write the rule in uv notation down before you start. The quotions rule is f( x ) I 9( x) I = Id I - IdI I1 2 Therefore with the given function (() : 5 af ( 7 * 2 + 1 )3 So, F ( x) = (7 *2 + 1)5 d ( 5) - 5 & (7. 2+1)3 ((7, 2 +1)372 f (x ) = (7 x2 + 1) 3 . 0 - 5 - 3 ( 7 x 2 + 1) 2 . (7 - 2 x 10) [(x) = 0- 210 x (7*2+122 (72 2+1 ). - 210 * (7 , 2 +1) (7 *211)4 The first derivative is t'() = -210x (7 x 2 + 1 )* 3 points b ) by rewriting the equation and then using chain rule. x" = man - given f(x ) . 5 (712:D)3 5 (7 x 2 + 1)-3 so , diff wr tox += 7, 2 +1 therefore df = d [ 5 ( 7 2 2 . 0 3 ] dr = d ( 7 3 2 +1 ) ax dx at = 7 . 2x+0 F ( x ) = 5 ( - 3t 4 ) Hx at F (W) - 70 * [- 3 ( 7 241) "] = 14X ax F' ( x ) = - 210 x ( 7 x 2 + 1 ) + So, F'(x ) = - 210 x using chainRule. ( 7 x2 +1)4 2 points C) Why would we prefer the second method in this case, but not in others? Give an example where we would prefer quotient rule