(a) If g is differentiable, the Reciprocal Rule says that g'(x) dx g(x) Use the Quotient Rule to prove the Reciprocal Rule. (b) Use the Reciprocal Rule to differentiate the function y = 1/(x* + x? + 1). (c) Use the Reciprocal Rule to verify that the Power Rule is valid for negative integers, that is, (r") = -nx*-1 dx for all positive integers n.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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(a) If g is differentiable, the Reciprocal Rule says that
g'(x)
dx g(x)
Use the Quotient Rule to prove the Reciprocal Rule.
(b) Use the Reciprocal Rule to differentiate the function
y = 1/(x* + x? + 1).
(c) Use the Reciprocal Rule to verify that the Power Rule
is valid for negative integers, that is,
(r") = -nx*-1
dx
for all positive integers n.
Transcribed Image Text:(a) If g is differentiable, the Reciprocal Rule says that g'(x) dx g(x) Use the Quotient Rule to prove the Reciprocal Rule. (b) Use the Reciprocal Rule to differentiate the function y = 1/(x* + x? + 1). (c) Use the Reciprocal Rule to verify that the Power Rule is valid for negative integers, that is, (r") = -nx*-1 dx for all positive integers n.
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