Q.40 Use the differentiation rules de... [FREE SOLUTION]

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Chapter 2: Q.40 (page 198)

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

Short Answer

Expert verified

The derivatives of the given function is $2 x + 2 - 9 x^{2}$

Step by step solution

Step1. Given information

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

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

Step2. finding the derivatives of the function

the given function is $f (x) = x^{2} + x (2 - 3 x^{2})$ . When opening the parenthesis in the given function multiplying x , we get

$f (x) = x^{2} + 2 x - 3 x^{3}$

Now we can find out the derivatives of this expansion form then,

localid="1649266685938" role="math" $\frac{d}{d x} (x^{2} + 2 x - 3 x^{3}) = \frac{d (x^{2})}{d x} + \frac{d (2 x)}{d x} - \frac{d (3 x^{3})}{d x} derivative of an identity function x, \frac{d (x)}{d x} = 1 so \frac{d (2 x)}{d x} = 2 \frac{d (x)}{d x} = 2 The derivative of \frac{d}{d x} (x^{n}) = {nx}^{n - 1}, for any non zero rational number n using power rule, then \frac{d (x^{2})}{d x} = 2 x \frac{d (3 x^{3})}{d x} = 3 \frac{d (x^{3})}{d x} = 3 脳 3 x^{2} = 9 x^{2} thus the derivative of given function, \frac{d}{d x} (x^{2} + x (2 - 3 x^{3}) = 2 x + 2 - 9 x^{2}$

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91影视

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

Short Answer

Step by step solution

Step1. Given information

Step2. finding the derivatives of the function

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91影视

Use the differentiation rules developed in this section to findthe derivatives of the functionsf(x)=x2+x(2-3x2)

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

Logic and Functions

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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