Find dy if y = (x³ + 4x)³dxSimplify completely. Do not multiply out any binomials raised to more than the 2nd power.

Answered: ddy if y= (x² + 4x)² dx Simplify…

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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Question

Find dy if y = (x³ + 4x)³
dx
Simplify completely. Do not multiply out any binomials raised to more than the 2nd power.

Expert Solution

Step 1: Rules for Derivative

y= $left parenthesis x cubed plus 4 x right parenthesis to the power of 8$

Rules $rightwards arrow$

(i) $fraction numerator d space over denominator d x end fraction left parenthesis x to the power of n right parenthesis equals n x to the power of n minus 1 end exponent$

(ii) $fraction numerator d space over denominator d x end fraction left parenthesis c o n s tan t right parenthesis equals 0$

(iii) $fraction numerator d space over denominator d x end fraction left parenthesis a. b right parenthesis equals a cross times fraction numerator d space over denominator d x end fraction left parenthesis b right parenthesis plus b cross times fraction numerator d space over denominator d x end fraction left parenthesis a right parenthesis$