generateSpecialFunction("x") generateSpecialFunction("x") FUNCN.fText FUNCN.ddxFText FUNCD.fText FUNCD.ddxFText funcNotation("x") function( a, b, c, d, e, min ) { // create fraction of the form ( (a)(b) + (c)(d) ) / e^2 var term1 = "(" + a + ")" + ( a === b ? "^2" : "(" + b + ")" ), term2 = "(" + c + ")" + ( c === d ? "^2" : "(" + d + ")" ); return "\\dfrac{" + term1 + min + term2 + "}{(" + e + ")^2}"; }

Find \displaystyle \frac{d}{dx}\biggl( \frac{FUNCN.fText}{FUNCD.fText} \biggr).

ANSWER( N_DF, D_F, D_DF, N_F, D_F, "-" )

• ANSWER( N_DF, D_DF, D_F, N_F, D_F, "-" )
• ANSWER( N_DF, D_F, D_DF, N_F, N_F, "-" )
• ANSWER( N_DF, D_DF, D_F, N_F, N_F, "-" )
• ANSWER( N_DF, D_F, D_DF, N_F, D_F, "+" )
• ANSWER( N_DF, D_DF, D_F, N_F, D_F, "+" )
• ANSWER( N_DF, D_F, D_DF, N_F, N_F, "+" )
• ANSWER( N_DF, D_DF, D_F, N_F, N_F, "+" )

Using the chain rule and the product rule, we know \displaystyle \frac{d}{dx\strut}\frac{f(x)}{g(x)} = \frac{f'(x)g(x) - g'(x)f(x)}{g(x){}^2}.

In this case,

\qquad f(x) = FUNCN.fText,

\qquad g(x) = FUNCD.fText.

Differentiate each function:

\qquad f'(x) = FUNCN.ddxFText,

\qquad g'(x) = FUNCD.ddxFText.

\qquad \dfrac{{(FUNCN.ddxFText)(FUNCD.fText) - (FUNCD.ddxFText)(FUNCN.fText)}}{(FUNCD.fText)^2}.