Homework Help is Here – Start Your Trial Now!
Math
Geometry
Consider the following proof of the Product Rule: f(r + h)g(z +h) – S(z)9(z) Remember that we can add zero to anything without changing its value. Therefore, we can write the above limit as f(z + h)g(x + h) – {(x}g{lz + h) + {(x}9(z + h) – ƒ(2)9(x) lim Splitting the limit of a sum into the sum of limits we get S(z + h)g(z+ h) – S(z)g(z+ h) (z)9(z +h) – f(z)9(x) lim + lim Factoring and writing the limit of a product as the product of limits we get 9(z + h) - g(z) - lim g(z+ + lim lim By the limit definition of the derivative this then gives Use a similar argument to prove the Quotieat Rule: 4 ())- I'(2)9(x) – S(x)d'(z) (g(z)) dz (9(r) Note: You are being asked to use the limit definition of the derivative to prove the quotient rule. Providing an example of how to use the quotient rule is not sufficient. Find f'(z) and "(=). (a) S(z) - Va (b) S(2) = If f is a differentiable function, find an expression for the derivative of the following functions. 1+ f(r) (a) y= (b) y- S(z)

Consider the following proof of the Product Rule: f(r + h)g(z +h) – S(z)9(z) Remember that we can add zero to anything without changing its value. Therefore, we can write the above limit as f(z + h)g(x + h) – {(x}g{lz + h) + {(x}9(z + h) – ƒ(2)9(x) lim Splitting the limit of a sum into the sum of limits we get S(z + h)g(z+ h) – S(z)g(z+ h) (z)9(z +h) – f(z)9(x) lim + lim Factoring and writing the limit of a product as the product of limits we get 9(z + h) - g(z) - lim g(z+ + lim lim By the limit definition of the derivative this then gives Use a similar argument to prove the Quotieat Rule: 4 ())- I'(2)9(x) – S(x)d'(z) (g(z)) dz (9(r) Note: You are being asked to use the limit definition of the derivative to prove the quotient rule. Providing an example of how to use the quotient rule is not sufficient. Find f'(z) and "(=). (a) S(z) - Va (b) S(2) = If f is a differentiable function, find an expression for the derivative of the following functions. 1+ f(r) (a) y= (b) y- S(z)

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
See similar textbooks
icon
Related questions
Question
Consider the following proof of the Product Rule: f(r + h)g(z +h) – S(z)9(z) Remember that we can add zero to anything without changing its value. Therefore, we can write the above limit as f(z + h)g(x + h) – {(x}g{lz + h) + {(x}9(z + h) – ƒ(2)9(x) lim Splitting the limit of a sum into the sum of limits we get S(z + h)g(z+ h) – S(z)g(z+ h) (z)9(z +h) – f(z)9(x) lim + lim Factoring and writing the limit of a product as the product of limits we get 9(z + h) - g(z) - lim g(z+ + lim lim By the limit definition of the derivative this then gives Use a similar argument to prove the Quotieat Rule: 4 ())- I'(2)9(x) – S(x)d'(z) (g(z)) dz (9(r) Note: You are being asked to use the limit definition of the derivative to prove the quotient rule. Providing an example of how to use the quotient rule is not sufficient. Find f'(z) and "(=). (a) S(z) - Va (b) S(2) = If f is a differentiable function, find an expression for the derivative of the following functions. 1+ f(r) (a) y= (b) y- S(z)
Transcribed Image Text:Consider the following proof of the Product Rule: f(r + h)g(z +h) – S(z)9(z) Remember that we can add zero to anything without changing its value. Therefore, we can write the above limit as f(z + h)g(x + h) – {(x}g{lz + h) + {(x}9(z + h) – ƒ(2)9(x) lim Splitting the limit of a sum into the sum of limits we get S(z + h)g(z+ h) – S(z)g(z+ h) (z)9(z +h) – f(z)9(x) lim + lim Factoring and writing the limit of a product as the product of limits we get 9(z + h) - g(z) - lim g(z+ + lim lim By the limit definition of the derivative this then gives Use a similar argument to prove the Quotieat Rule: 4 ())- I'(2)9(x) – S(x)d'(z) (g(z)) dz (9(r) Note: You are being asked to use the limit definition of the derivative to prove the quotient rule. Providing an example of how to use the quotient rule is not sufficient. Find f'(z) and "(=). (a) S(z) - Va (b) S(2) = If f is a differentiable function, find an expression for the derivative of the following functions. 1+ f(r) (a) y= (b) y- S(z)
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer