Question

Question Find the derivative of the function ( y=frac{cos ^{3}(x) sin ^{3}(x)}{left(2 x^{3}+1 ight)^{2}} ) using logarithmic differentiation. Be sure to include parentheses around the arguments of any trigonometric functions in your answer. Provide your answer below: [ y^{prime}=square ]

          Question
Find the derivative of the function ( y=frac{cos ^{3}(x) sin ^{3}(x)}{left(2 x^{3}+1
ight)^{2}} ) using logarithmic differentiation. Be sure to include parentheses around the arguments of any trigonometric functions in your answer.

Provide your answer below:
[
y^{prime}=square
]

$Question Find the derivative of the function ( y=fraccos ^3(x) sin ^3(x)left(2 x^3+1 ight)^2 ) using logarithmic differentiation. Be sure to include parentheses around the arguments of any trigonometric functions in your answer. Provide your answer below: [ y^prime=square ]$

Added by Jason B.

Calculus an Applied Approach

Ron Larson, David C, Falvo 8th Edition

Chapter 8

Instant Answer

Solved by Expert Gregory Higby

01/22/2024

Step 1

This is the essence of logarithmic differentiation. We have: \[ y = \frac{\cos^3(x) \sin^3(x)}{(2x^3 + 1)^2} \] Taking the natural logarithm of both sides gives us: \[ \ln(y) = \ln\left(\frac{\cos^3(x) \sin^3(x)}{(2x^3 + 1)^2}\right) \] Show more…

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