Short Answer

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
$f (x) = x {(3 x^{2} + 1)}^{9}$

The required answer is ${(3 x^{2} + 1)}^{9} + 54 x^{2} {(3 x^{2} + 1)}^{8}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

The given function is $f (x) = x {(3 x^{2} + 1)}^{9}$

Step 2. Calculation

Differentiate both the sides with respect to x, we get,

$f' (x) = \frac{d}{d x} (x) {(3 x^{2} + 1)}^{9} + x (\frac{d}{d x} {(3 x^{2} + 1)}^{9}) = {(3 x^{2} + 1)}^{9} + x (9 {(3 x^{2} + 1)}^{9 - 1} \frac{d}{d x} (3 x^{2} + 1)) = {(3 x^{2} + 1)}^{9} + x (9 {(3 x^{2} + 1)}^{8} (\frac{d}{d x} 3 x^{2} + \frac{d}{d x} 1)) = {(3 x^{2} + 1)}^{9} + x (9 {(3 x^{2} + 1)}^{8} (3 (2 x))) = {(3 x^{2} + 1)}^{9} + 54 x^{2} {(3 x^{2} + 1)}^{8}$

Find Study Materials for

Create Study Materials

Select your language

Calculus

Answers without the blur.

Short Answer

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
$f (x) = x {(3 x^{2} + 1)}^{9}$

Step by Step Solution

Step 1. Given Information

Step 2. Calculation

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Calculus

Answers without the blur.

Short Answer

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating. f(x)=x(3x2+1)9

Step by Step Solution

Step 1. Given Information

Step 2. Calculation

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
$f (x) = x {(3 x^{2} + 1)}^{9}$