Determine whether the following statements are true and give an explanation or counterexample. a. For any equation

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Determine whether the following statements are true and give an explanation or counterexample.

a. For any equation containing the variables x and y, the derivative dy/dx can be found by first using algebra to rewrite the equation in the form y = f(x).

b. For the equation of a circle of radius r, x2 + y2 = r2, we have dy/dx = -x/y, for y ≠ 0 and any real number r > 0.

c. If x = 1, then by implicit differentiation, 1 = 0.

d. If xy = 1, then y' = 1/x.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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