3.7: Implicit Differentiation

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Jan 31, 2024
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- 3.6: Derivatives as Rates of Change
- 3.8: Derivatives of Inverse Functions

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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.

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