First slide

Derivatives

Question

$If 2 x^{2} - 3 x y + y^{2} + x + 2 y - 8 = 0 then \frac{d y}{d x} =$

Moderate

A

$\frac{3 y - 4 x - 1}{2 y - 3 x + 2}$
B

$\frac{3 y + 4 x + 1}{2 y + 3 x + 2}$
C

$\frac{3 y - 4 x + 1}{2 y - 3 x - 2}$
D

$\frac{3 y - 4 x + 1}{2 y + 3 x + 2}$

Solution

$\begin{array}{l} f_{x} = 0 \Rightarrow 4 x - 3 y + 1 = 0 \\ f y = 0 \Rightarrow - 3 x + 2 y + 2 = 0 \\ \frac{d y}{d x} = - \frac{f x}{f y} = \frac{3 y - 4 x - 1}{2 y - 3 x + 2} \end{array}$

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