Mathematics

Mathematics

Problem

The answers are in Chapter 24. 4. Find dydx\frac{d y}{d x} if xy2−4x3y2=−3x y^{2}-4 x^{3} y^{2}=-3 at (1,1)(1,1). (A) −116-\frac{11}{6} (B) −611-\frac{6}{11} (C) 1013\frac{10}{13} (D) 1310\frac{13}{10} (A) −116-\frac{11}{6} (B) −611-\frac{6}{11} (C) 1013\frac{10}{13} (D) 1310\frac{13}{10}
Intuitive explanation

This is an implicit differentiation problem where yy is tangled up with xx in an equation, so you can't easily solve for yy first. Differentiate both sides with respect to xx, treating yy as a function of xx and applying the product rule and chain rule wherever yy appears. Then substitute the point (1,1)(1,1) to find the numerical value of the slope at that specific location.

Intuitive explanation

This is an implicit differentiation problem where yy is tangled up with xx in an equation, so you can't easily solve for yy first. Differentiate both sides with respect to xx, treating yy as a function of xx and applying the product rule and chain rule wherever yy appears. Then substitute the point (1,1)(1,1) to find the numerical value of the slope at that specific location.

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