Implicit Differentiation (Calculus I)
Free printable university Calculus I worksheet: finding dy/dx for curves defined implicitly (circles, ellipses, hyperbolas and cubics), and evaluating the slope at a given point on the curve. Every slope verified against the curve numerically.
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Calculus I · Math worksheet
Name
Date
Math
Implicit Differentiation
Each curve defines y implicitly as a function of x near the given point. Differentiate both sides with respect to x (remembering dy/dx wherever y appears), solve for dy/dx, then evaluate at the point.
- 1.The curve + 3y^2 = 52 passes through (2, 4). Use implicit differentiation to find dy/dx, then evaluate it at that point.
- 2.The curve 2x^2 + 3y^2 = 30 passes through (3, 2). Use implicit differentiation to find dy/dx, then evaluate it at that point.
- 3.The curve 4x^2 + 3y^2 = 84 passes through (3, 4). Use implicit differentiation to find dy/dx, then evaluate it at that point.
- 4.The curve xy = -15 passes through (-3, 5). Use implicit differentiation to find dy/dx, then evaluate it at that point.
- 5.The curve xy = 4 passes through (-2, -2). Use implicit differentiation to find dy/dx, then evaluate it at that point.
- 6.The curve + xy + = 28 passes through (2, 4). Use implicit differentiation to find dy/dx, then evaluate it at that point.
- 7.The curve + xy + = 9 passes through (3, -3). Use implicit differentiation to find dy/dx, then evaluate it at that point.
- 8.The curve + y = 2x^2 - 8 passes through (3, 2). Use implicit differentiation to find dy/dx, then evaluate it at that point.
- 9.The curve + 2y = 2x^2 + 31 passes through (-1, 3). Use implicit differentiation to find dy/dx, then evaluate it at that point.
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