Differentiate. y=ln(x^4)/(2)

Name: Problem 60, Chapter 3: Calculus and Its Applications
Uploaded: 2020-10-21T23:00:29-08:00
Duration: 50 s
Channel: Linh Vu
Description: Differentiate. y=ln(x^4)/(2)

step 1 we recall about the L -LL of the U derivative, which we can include the U -prem over U. In this

Question

Differentiate. $$y=\ln \frac{x^{4}}{2}$$

   Differentiate.
$$y=\ln \frac{x^{4}}{2}$$

Calculus and Its Applications

Marvin L. Bittinger,… 10th Edition

Chapter 3, Problem 60

Instant Answer

Solved by Expert Linh Vu

10/21/2020

Step 1

The property states that $\ln \frac{a}{b} = \ln a - \ln b$. Applying this property to the given function, we get: $$y = \ln x^{4} - \ln 2$$ Show more…

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Differentiate. $$y=\ln \frac{x^{4}}{2}$$

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Key Concepts

Properties of Logarithms

Properties of logarithms, such as ln(a/b) = ln(a) - ln(b) and ln(a^n) = n*ln(a), are useful for simplifying complex logarithmic expressions before differentiation. Simplification makes the differentiation process more straightforward by reducing it to simpler terms.

Logarithmic Differentiation

This concept involves finding the derivative of functions that contain logarithms. The derivative of ln(u) with respect to x uses the formula (1/u)*du/dx, which is particularly useful when the argument of the logarithm is a function of x.

Chain Rule

The chain rule is applied when differentiating composite functions. In the context of the logarithm, after identifying the inner function u(x) inside the logarithm, the derivative is computed as the derivative of the outer function (ln(u)) multiplied by the derivative of the inner function.

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