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Unformatted text preview: Worksheet for Section 2.6 Implicit Diﬀerentiation
V63.0121, Calculus I Spring 2010
For each of the two problems below: (a) Find dy/dx by diﬀerentiating implicitly. (b) Solve the equation for y as a function of x, and ﬁnd dy/dx explicitly from that equation (c) Conﬁrm that the two are equal by expressing the derivative in (a) as a function of x alone. 1. x + xy − 2x3 = 2 2. √ y − sin x = 3. 1 y 2 3. Find the slope of the line tangent to the curve 1 2(x2 + y 2 )2 = 25(x2 − y 2 ) −3 at the point (3, 1). −2 −2 −1 −1 1 2 3 x 4. Find all horizontal and vertical tangents to the curve x2 y − 4y = x2 . 2 ...
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This note was uploaded on 07/19/2010 for the course MATHEMATIC V63.0121 taught by Professor Leingang during the Spring '09 term at NYU.
- Spring '09