3.7: Implicit Differentiation
- Page ID
- 144211
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- Use implicit differentiation to find \(\dfrac{dy}{dx}\) for \(x^2 - y^2 = 4\).
- Use implicit differentiation to find \(\dfrac{dy}{dx}\) for \(6x^2 + 3y^2 = 12\).
- Use implicit differentiation to find \(\dfrac{dy}{dx}\) for \(x^2y = y - 7\).
- Use implicit differentiation to find \(\dfrac{dy}{dx}\) for \(3x^3 + 9xy^2 = 5x^3\).
- Use implicit differentiation to find \(\dfrac{dy}{dx}\) for \(xy - \cos(xy) = 1\).
- Use implicit differentiation to find \(\dfrac{dy}{dx}\) for \(y\sqrt{x + 4} = xy + 8\).
- Use implicit differentiation to find \(\dfrac{dy}{dx}\) for \(-xy - 2 = \dfrac{x}{7}\).
- Use implicit differentiation to find \(\dfrac{dy}{dx}\) for \(y \sin(xy) = y^2 + 2\).
- Use implicit differentiation to find \(\dfrac{dy}{dx}\) for \(\dfrac{y}{x + y} = \tan(x + y)\).
- Find the equation of the line tangent to \(x^4y - xy^3 = -2\) at the point \((-1, -1)\).
- Find the equation of the line tangent to \(x^2y^2 + 5xy = 14\) at the point \((2, 1)\).
- Find the equation of the line tangent to \(\tan(xy) = y\) at the point \(\left(\dfrac{\pi}{4}, 1\right)\).
- Find the equation of the line tangent to \(xy^2 + \sin(\pi y) - 2x^2 = 10\) at the point \((2, -3)\).
- Find all points on the graph of \(y^3 - 27y = x^2 - 90\) at which the tangent line is vertical.