Chapter 2: Q.37 (page 198)

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

Short Answer

Expert verified

The derivative of the given function is $12 x$

Step by step solution

Step1. Given information

The function $f (x) = 2 (1 + 3 x^{2})$

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

Step2. finding the derivatives of the function

Based on the question

$f (x) = 2 (1 + 3 x^{2}), we can open the parenthesis by multipying 2 we get, = 2 + 6 x^{2},$

Now using the differentiation rule to find the derivate of the given function , we get

$\frac{d}{d x} (2 + 6 x^{2}) = \frac{d (2)}{d x} + \frac{d (6 x^{2})}{d x} derivative of a constant is 0, so \frac{d (2)}{d x} = 0 and \frac{d (6 x^{2})}{d x} = 6 \frac{d (x^{2})}{d x}, \sin c e derivative of \frac{d}{d x} (x^{n}) = n x^{n - 1}, for any non zero rational number n using power rule = 6 \times 2 x = 12 x th e n the derivative of given function, \frac{d}{d x} 2 (1 + x^{2}) = 0 + 12 x = 12 x$

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

Short Answer

Step by step solution

Step1. Given information

Step2. finding the derivatives of the function

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

Pure Maths

Probability and Statistics

Statistics

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Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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