Find the derivative’s 2х — 434. y =x2 +2L

The function is y=2x-4x2+23. Obtain the derivative of the function y=2x-4x2+23 using chain rule as…

Answered: з /2х — 4 4. У 3 х2 + 2

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter2: Solving Linear Inequalities

Section: Chapter Questions

Problem 4CR

See similar textbooks

Related questions

Concept explainers

Question

Find the derivative’s

Expert Solution

Step 1

The function is $y = \sqrt[3]{\frac{2 x - 4}{x^{2} + 2}}$ .

Obtain the derivative of the function $y = \sqrt[3]{\frac{2 x - 4}{x^{2} + 2}}$ using chain rule as follows.

$\begin{array}{rcl} \frac{d y}{d x} & = & \frac{d}{d x} (\sqrt[3]{\frac{2 x - 4}{x^{2} + 2}}) \\ = & \frac{d}{d x} {(\frac{2 x - 4}{x^{2} + 2})}^{\frac{1}{3}} \\ = & \frac{1}{3} {(\frac{2 x - 4}{x^{2} + 2})}^{- \frac{2}{3}} \frac{d}{d x} (\frac{2 x - 4}{x^{2} + 2}) \\ = & \frac{1}{3 {(\frac{2 x - 4}{x^{2} + 2})}^{\frac{2}{3}}} \frac{d}{d x} (\frac{2 x - 4}{x^{2} + 2}) \dots (1) \end{array}$

Step 2

Now find the value of $\frac{d}{d x} (\frac{2 x - 4}{x^{2} + 2})$ using the quotient equation.

$\begin{array}{rcl} \frac{d}{dx} (\frac{2 x - 4}{x^{2} + 2}) & = & \frac{\frac{d}{dx} (2 x - 4) (x^{2} + 2) - \frac{d}{dx} (x^{2} + 2) (2 x - 4)}{{(x^{2} + 2)}^{2}} \\ = & \frac{2 (x^{2} + 2) - 2 x (2 x - 4)}{{(x^{2} + 2)}^{2}} \\ = & \frac{- 2 x^{2} + 8 x + 4}{{(x^{2} + 2)}^{2}} \end{array}$

Step by step

Solved in 3 steps

Knowledge Booster

$Single Variable$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Big Ideas Math A Bridge To Success Algebra 1: Stu…

Algebra

ISBN:

9781680331141

Author:

HOUGHTON MIFFLIN HARCOURT

Publisher:

Houghton Mifflin Harcourt