💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

Compute the derivative of the given function $f(x)$ by $(a)$ multiplying and then differentiating and (b) using the product rule. Verify that (a) and (b) yield the same result.$f(x)=(x+1)\left(x^{2}-x+1\right)$

Calculus 1 / AB

Chapter 2

THE DERIVATIVE

Section 4

The Product and Quotient Rules

Functions

Limits

Derivatives

Differentiation

Continuous Functions

Applications of the Derivative

Missouri State University

Oregon State University

Idaho State University

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:19

Compute the derivative of …

00:57

01:27

02:39

Use the quotient rule to s…

01:14

Derivatives by two differe…

01:35

Find the derivative of eac…

Use the Quotient Rule to c…

01:06

Find the derivative of the…

03:54

Calculate the derivative i…

01:12

Okay, so we went to you. So we want to find our derivative here by first multiplying out what we have that's going to be X cubed. Minus X Word was axe and plus X squared minus X and then plus one. So let's combine like change. Do we get X cubed? X squared cancels on X and and we just have cost one. So finding are derivative of this time. Is he able to three x squared plus one. Now we want to find our derivative by taking our product rule. So the derivative this term that's just one times X squared minus X. What's one and we have plus Joe this time That's two x minus one climbs exports one. Okay, so let's multiply out one we have you have plus two x squared plus two x minus X and in minus one. Now let's combine like terms. We have one plus two x words. That's three exc word and then plus X actually, um, used to excess cancel. So we have plus two X. That's weird. We should have a plus one if I'm doing this correctly, so it's double check, so we have to It squared plus two acts minus minus one. And this year is X squared minus X minus plus one. Eso yet are actually these two service Cancel out One more thing. Um, so we have This is my is two x plus two x I actually should be so right. That's right. So when we take derivative of this term derivative of a constant in sterile so sorry, but that were actually left with three X squared.

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Compute the derivative of the given function $f(x)$ by $(a)$ multiplying and…

Use the quotient rule to show that the derivative of $[g(x)]^{-1}$ is $-g^{\…

Derivatives by two different methodsa. Use the Product Rule to find the …

Find the derivative of each function.$$f(x)=(x+2) \frac{x^{2}-1}{x^{2}+x…

Use the Quotient Rule to calculate the derivative.\begin{equation}f(…

Find the derivative of the following functions.$$f(x)=\left(1+\frac{1}{x…

Calculate the derivative in two ways. First use the Product or Quotient Rule…

Find the derivative of each function.$$f(x)=\frac{2 x}{x^{2}+1}$$