Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Use the properties of logarithms to find the derivative. Hint: It might be easier if you use the properties of logarithms first.$$y=\ln \sqrt[3]{5 x+7}$$

$$\frac{5}{3(5 x+7)}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Campbell University

Oregon State University

McMaster University

Lectures

01:50

Use the properties of loga…

02:53

02:27

03:52

01:18

02:35

Use logarithmic differenti…

01:22

02:22

02:09

01:19

04:00

Find the derivative of $y$…

02:32

01:13

03:28

Find the derivative using …

eso were asked to find the derivative of the natural log of the cube root of five X plus seven. And I do like the note and here that it says it's easier if you rewrite this using your law of logs, which is that five X plus seven could be written to the one third power. So then, from there you can bring that one third in front eso. We're looking at one third natural log of five X plus seven. If you're curious, why that's beneficial is because if you don't, you have a chain rule inside of a chain rule inside of a Well, I guess the largest function to be that thing. Whereas over here it's just one channel eso I think we're ready to just get into the derivative, which is, uh, I know I'm not lining this up very well because I'm looking at this problem over here where that one third stays the same now, the derivative of natural log is one over the function inside, So that would be five X plus seven. Um, but then, from there you have to multiply by the derivative of the inside. Well, the derivative of five Xs five, uh, and then drove to the 70 So there's nothing to right. There s o, I guess from there we're ready to write the final answer. Now, I would just leave it as you know, one times one times 5/1 and then three times the quantity of five X plus seven. I know some people might distribute that three into the problem. Um, but you're just making more work, and you're more likely to make a mistake. If you do that, just sleep. Your answer like this, and we're good.

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:16

Determine the equation of the tangent line at the given $x$ -coordinate.…

03:36

The population is growing at about $6 \%$ each year. If the population in 20…

01:02

Verify that $f$ and $g$ are inverse functions using the composition property…

Use -0.000121 as the decay constant for Carbon 14.If an ancient wooden a…

00:43

$f(x, y)=4 x^{3} y^{2}$ determine (a) $f(3,2),(b) f(2,5)$

02:15

Use the properties of logarithms to find the derivative. Hint: It might be e…

02:05

Evaluate the given integral.$$\int\left(3 x^{5}+1\right)^{8} 15 x^{4} d …

02:39

Evaluate the given integral.$$\int_{-1}^{0} x^{2}\left(2 x^{3}+1\right)^…

03:06

Find and classify, using the second partial derivative test, the critical po…

04:04

Find the partial derivatives with respect to (a) $x$ and (b) $y$.$$f(x, …