AP Calculus BC 3.2: Implicit Differentiation

Practise AP Calculus BC 3.2 by differentiating implicit equations with chain, product and trigonometric rules, then evaluating dy/dx or tangent slopes at given points.

Exam points

Apply chain and product rules to algebraic, trigonometric or logarithmic implicit equations.
Isolate dy/dx after differentiating, then evaluate a derivative or tangent slope at a given point.

[Maximum number: 1]

If y is a differentiable function of x, then the slope of the curve of $x y^{2}$ $-2 y+4 y^{3}=6$ at the point where y=1 is

$-\frac{1}{18}$

$\frac{5}{18}$

$\frac{1}{3}$

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FUN-3.D—Calculate derivatives of implicitly defined functions question 1