Q.39 Use the differentiation rules de... [FREE SOLUTION]

91影视

Chapter 2: Q.39 (page 198)

Use the differentiation rules developed in this section to find
the derivatives of the functions
$f (x) = 2 (3 x + 1) - 4 x^{5}$

Short Answer

Expert verified

The derivatives of the given function is $6 - 20 x^{4}$

Step by step solution

Step1. Given information

Here given function is $f (x) = 2 (3 x + 1) - 4 x^{5}$

We need to find out the derivatives of the given function.

Step2. finding the derivatives of the function

In this question given function is $f (x) = 2 (3 x + 1) - 4 x^{5}$ .

Here first we can open the parenthesis by multiplying 2 then we get

$f (x) = 6 x + 2 - 4 x^{5}$ .Now we can find derivative of this function using differentiation rules , then

localid="1649266847729" $\frac{d}{d x} (6 x + 2 - 4 x^{5}) = \frac{d (6 x)}{d x} + \frac{d (2)}{d x} - \frac{d (4 x^{5})}{d x} derivative of a constant is 0, so \frac{d (2)}{d x} = 0 and \frac{d (4 x^{5})}{d x} = 4 脳 \frac{d (x^{5})}{d x}, since derivative of \frac{d}{d x} (x^{n}) = {nx}^{n - 1}, for any non zero rational number n using power rule = 4 脳 5 x^{4} = 20 x^{4} \frac{d (6 x)}{d x} = 6 \frac{d (x)}{d x}, since derivative of an identity function x, \frac{d (x)}{d x} = 1 = 6 then the derivative of given function, \frac{d}{d x} 2 (3 x + 1) - 4 x^{5} = 6 + 0 - 20 x^{4} = 6 - 20 x^{4}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Use the differentiation rules developed in this section to find
the derivatives of the functions
$f (x) = 2 (3 x + 1) - 4 x^{5}$

Short Answer

Step by step solution

Step1. Given information

Step2. finding the derivatives of the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Geometry

Discrete Mathematics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

91影视

Use the differentiation rules developed in this section to findthe derivatives of the functionsf(x)=2(3x+1)-4x5

Short Answer

Step by step solution

Step1. Given information

Step2. finding the derivatives of the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Geometry

Discrete Mathematics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Use the differentiation rules developed in this section to find
the derivatives of the functions
$f (x) = 2 (3 x + 1) - 4 x^{5}$