find-the-derivatives-of-the-given-functions-yln-leftx-x2right3-3

Question

Find the derivatives of the given functions.
$$y=\ln \left(x-x^{2}\right)^{3}$$

Tyler Moulton · Accepted Answer

we want to find dy dx for the function. Why is equal to the natural algorithm of x minus x squared cute. This question is since their knowledge of differentiation shortcuts related transcendental functions in particular those were logarithmic functions. So we have to note relevant rules to proceed on the left. I have the rules protecting DDX of log B of U n L. Interview on the right rules 123 are respectively the power rule. Product rule in changeable for this function Y equals x minus x, cuba square or rather cute. We already have it in its most easily defensible forum and we see that we&#x27;re going to have to use rule zero G. D. Exelon you to solve for you is x minus X squared cute. Thus will have to also invoke the chain rule. So do I. D. S is one over you? One by one over X minus X squared cute times the U D X. Which is by the channel three times x minus x squared square terms one minus two X. Thus we have solution. Dy dx is equal to three minus six X divided by x minus x squared

Robert Daugherty · Answer

problem Number 19 section 4.5 Again. Everything in the section derivatives of functions with natural logs. So let&#x27;s consider why is equal to three X squared divided by natural log of X. So what if I got going on there? I need to know how to take derivatives. A polynomial sze logarithms and quotients. Okay, keep in mind as many times as you can. If this is not your muscle memory, how do you deal with the quotient? The derivative of quotient is f prime G minus G prime F over G squared. I&#x27;m looking at a problem where where my numerator is three x squared, whereby no nominator is natural Log of X. So I just need to plug into the formula there for the quotient rule. So in this case, I&#x27;m going to find that why Prime is equal to f Prime G driven of the numerator is gonna be, what, six x times the denominator as natural log of x minus. Okay, the derivative of the denominator. That&#x27;s simply one over x times. And you, writer, which is three x squared. All of that over the denominator squared. So I&#x27;ve got some simplification here. Why prime will be equal to six x natural log of X minus three X squared over X is just simply going to be three x so three x all of that divided by the natural log of X squared and that is it.

Oswaldo Jiménez · Answer

going to find derivative off the function y equals three times six square to bottom unnatural algorithm of X And here we have, ah, think ocean of two functions and a constant three in the numerator. So first we take the constant out, so off the derivative of y respective X equal to three times derivative respected eggs off the Kocian X square, divided by natural algorithm affects. And so this is equal to three times the fraction in whose new rotary&#x27;s natural rhythm of X times the derivative respective eggs off three times Sorry Off X square, minus X squared times. The derivative respected picks off the natural algorithm of X divided by the natural rhythm of X square. And then this is equal to three times the&#x27;s A river to ah, here is to turn six and that times natural rhythm FX minus X squared times the derivative off. That&#x27;s what the volume of exits one over eggs and that divided by natural algorithm of x square. So this is equal to three times to turn sex. Natural algorithm of ex miners and Khiry simplify X squared to better my ex, this ex and that you read about the natural rhythm of X Square and then we can take out. Come on factor X. In the numerator we get three times six times two times Natural rhythm affects minus one, divided by the natural terrorism of eggs square. So the derivative of the given fashion Why respective X is equal to three times six times two times natural rhythm of eggs minus one, divided by the natural algorithm of X square.

Robert Daugherty · Answer

section 3.6 problem 35. We&#x27;re dealing with derivatives that involve the use of the chain role. And you see this first term, not only will it be, change will also be the product rule, So why prime going to be equal to use treat? It is a product. The derivative of X is one So times e to the minus X plus X now the derivative of E to the minus sex That&#x27;s gonna be e to the minus. X times the derivative of minus X which is minus one. And this move onto this next term the derivatives gonna B e to the X cube times The derivative of X cubed, which is three x squared Oculus has done, is just now combining like terms. So why prime is equal to e to the minus x minus x e to the minus X was three x squared you to the X Cubed. It looks like the only further simplification is I can factor out of e to the minus x here. So why prime is e to the minus X and then one minus X plus three x squared you to the X cubed and that&#x27;s our final answer

Runpeng Li · Answer

so four problem seven function were given. Here is why today, why is equal to two times X cube so B y d X? That is a derivative of dysfunction? We&#x27;ll be three times two. That&#x27;s six coefficient and the power will be three minus one. So that&#x27;s two, and this is

Stephanie Martin · Answer

Okay, let&#x27;s find the derivative, Um, of why equals two X cubed. Using the limit definition of the derivative, um, we will get the limit as h goes to zero of why of x plus h, which I expanded up there using, um, the binomial theorem and then distributing in the two. That&#x27;s the quickest way to do it. Um And then also, I&#x27;m gonna write this as one over h times and then two x cubed, plus six each x squared and then minus Why so minus two x cubed, no thes cancel and then notice every term. Now hasn&#x27;t each left in it. So I&#x27;m going to factor that out. Now. These ages cancel, which was my objective. And now I can plug in that zero for age. So then I end up with six x squared, plus six times zero times x plus two times zero squared. Which means that D Y d eggs or the derivative of y with respect to X is equal to six x squared. And that is it

Problem

Find the derivatives of the given functions. $$s=…

Problem 13 Easy Difficulty

Find the derivatives of the given functions.
$$y=\ln \left(x-x^{2}\right)^{3}$$

Answer

$\frac{d y}{d x}=\frac{3(1-2 x)}{x-x^{2}}$

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Calculus 1 / AB Educators

Catherine R.

Kayleah T.

Caleb E.

Kristen K.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 27

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Caleb E.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$\frac{d y}{d x}=\frac{3(1-2 x)}{x-x^{2}}$

Basic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Caleb E.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Caleb E.

Kristen K.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus