Without evaluating derivatives, which of the functions 10 10 10 10 g(x) = 2x ,h(x) = x + 2, p(x) = x ? ln 2 have the same derivative as f(x) = x
Solution 25E Step 1 In this problem we have to find which of the given functions have same derivative as f(x) = x10 by using the fact that “Two differentiable functions, that differ by a constant always have the same derivative” … (1) First let us consider f(x)and g(x) Given f(x) = x , g(x) = 2x 10 10 10 f(x)g(x) = x 2x 10 = x f(x)g(x) = x where x is a function of xand is not a constant. Therefore f(x)and g(x)does not have same derivative. Step 2 Now consider f(x)and h(x) Given f(x) = x , h(x) = x +20 f(x)h(x) = x 10 (x +2) 10 10 = x x 2 = 2 f(x)h(x) = 2where 2is a constant. Therefore by ( 1) we get, f(x)and h(x)have same derivative.
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
The full step-by-step solution to problem: 25E from chapter: 4.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: derivative, Derivatives, evaluating, functions. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Since the solution to 25E from 4.6 chapter was answered, more than 279 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Without evaluating derivatives, which of the functions 10 10 10 10 g(x) = 2x ,h(x) = x + 2, p(x) = x ? ln 2 have the same derivative as f(x) = x” is broken down into a number of easy to follow steps, and 33 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.