Recall the Powers of x Rule: Iff(x) = xnwhere n is a real number, thenf '(x) = nxn − 1.Apply the Powers of x Rule toC = 0.22W1.57to find the derivative of C with respect to W. Write the exponent on W as its new coefficient and reduce the exponent by 1. Without rounding, find the product of the coefficient of the rate of change function and simplify the exponent.ddW[C] = ddW 0.22W1.57 Recall the Powers of x Rule: If f(x)x" where n is a real number, then f'(x)nx" - 1.Apply the Powers of x Rule to C = 0.22W'·57 to find the derivative of C with respect to W. Write the exponenton W as its new coefficient and reduce the exponent by 1. Without rounding, find the product of the coefficientof the rate of change function and simplify the exponent.dd0.22WdWdWdC1.57 - 1= 0.22 ·1.57dWdC|× )wo.570.345=dWRecall that W is the boweight of a fiddler crab, and note that W and w represent different variables inmathematics.Thus, for C = 0.22w1.57, the function that gives the rate of change of claw weight to body weight isdCdW0.345и0.57

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Answered: Recall the Powers of x Rule: If f(x) x"…

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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Recall the Powers of x Rule: If

f(x) = xⁿ

where n is a real number, then

f '(x) = nx^{n − 1}.

Apply the Powers of x Rule to

C = 0.22W^1.57

to find the derivative of C with respect to W. Write the exponent on W as its new coefficient and reduce the exponent by 1. Without rounding, find the product of the coefficient of the rate of change function and simplify the exponent.

[C]

0.22W^1.57

Recall the Powers of x Rule: If f(x)
x" where n is a real number, then f'(x)
nx" - 1.
Apply the Powers of x Rule to C = 0.22W'·57 to find the derivative of C with respect to W. Write the exponent
on W as its new coefficient and reduce the exponent by 1. Without rounding, find the product of the coefficient
of the rate of change function and simplify the exponent.
d
d
0.22W
dW
dW
dC
1.57 - 1
= 0.22 ·
1.57
dW
dC
|× )wo.57
0.345
=
dW
Recall that W is the bo
weight of a fiddler crab, and note that W and w represent different variables in
mathematics.
Thus, for C = 0.22w1.57, the function that gives the rate of change of claw weight to body weight is
dC
dW
0.345и0.57

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