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(a) Find y' by solving the equation for y and d (b) Find y' by implicit differentiation. (c) Check that the derivatives in (a) and (b) ar 1. =D1 2. z² + y³ = 4

(a) Find y' by solving the equation for y and d (b) Find y' by implicit differentiation. (c) Check that the derivatives in (a) and (b) ar 1. =D1 2. z² + y³ = 4

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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Question
For problems 1- 3 do each of the following. (a) Find y' by solving the equation for y and differentiating directly. (b) Find y' by implicit differentiation. (c) Check that the derivatives in (a) and (b) are the same. 1. 2. z + y* = 4 3. z? + y? = 2 4. 2y3 + 4x? – y = x° 5. 4x²y" – 2x = x° + 4y³
Transcribed Image Text:For problems 1- 3 do each of the following. (a) Find y' by solving the equation for y and differentiating directly. (b) Find y' by implicit differentiation. (c) Check that the derivatives in (a) and (b) are the same. 1. 2. z + y* = 4 3. z? + y? = 2 4. 2y3 + 4x? – y = x° 5. 4x²y" – 2x = x° + 4y³
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