For the curve defined by

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

For the curve defined by x2+xy+y2=7x^{2}+xy+y^{2}=7, which of the following expressions equals d2ydx2\dfrac{d^{2}y}{dx^{2}} in terms of xx and yy? (a) 42(x+2y)3\displaystyle \frac{42}{(x+2y)^{3}} (b) −42(2x+y)3\displaystyle -\frac{42}{(2x+y)^{3}} (c) 2(x−y)(x+2y)2−2(2x+y)2(x+2y)3\displaystyle \frac{2(x-y)}{(x+2y)^{2}}-\frac{2(2x+y)^{2}}{(x+2y)^{3}} (d) −42(x+2y)2\displaystyle -\frac{42}{(x+2y)^{2}}

Related theory

Browse the problem library