Implicit Differentiation

AP Calculus AB· difficulty 3/5

xy + y^2 = 8

A
$-\tfrac{2}{5}$
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B
$\tfrac{2}{5}$
C
$-2$
D
$-\tfrac{1}{5}$

Explanation

y + xy' + 2y y' = 0 \Rightarrow y'(x + 2y) = -y \Rightarrow y'(1, 2) = -2/(1+4) = -2/5

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