Show work, thank you! 7. Find the following derivatives.a)In(x² + 1)dxc) y = 4log3 (x²)b) E = 25,000 101.5Md) Use logarithmic differentiation to findthe derivative.x8c06³xy = √x-1

Answered: 7. Find the following derivatives. a)…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Show work, thank you!

7. Find the following derivatives.
a)In(x² + 1)
dx
c) y = 4log3 (x²)
b) E = 25,000 101.5M
d) Use logarithmic differentiation to find
the derivative.
x8c06³x
y = √x-1

Expert Solution

Step 1: Part(a)

$y apostrophe equals fraction numerator d over denominator d x end fraction open parentheses ln open parentheses x squared plus 1 close parentheses close parentheses$

Find the derivative.

$y apostrophe equals fraction numerator 1 over denominator x squared plus 1 end fraction fraction numerator d over denominator d x end fraction open parentheses x squared plus 1 close parentheses y apostrophe equals fraction numerator 1 over denominator x squared plus 1 end fraction open parentheses 2 x plus 0 close parentheses y apostrophe equals fraction numerator 1 over denominator x squared plus 1 end fraction open parentheses 2 x close parentheses y apostrophe equals fraction numerator 2 x over denominator x squared plus 1 end fraction$