1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aleks [24]
3 years ago
5

If f(x) = 9x10 tan−1x, find f '(x).

Mathematics
1 answer:
djverab [1.8K]3 years ago
7 0

Answer:

\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:                                                           \displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)  

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]:                                                                             \displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = 9x^{10} \tan^{-1}(x)

<u>Step 2: Differentiate</u>

  1. [Function] Derivative Rule [Product Rule]:                                                   \displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]
  2. Rewrite [Derivative Property - Multiplied Constant]:                                  \displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]
  3. Basic Power Rule:                                                                                         \displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]
  4. Arctrig Derivative:                                                                                         \displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

You might be interested in
How do you find the answer
liubo4ka [24]
It is  E  X= 22

J LINE SUPPLEMENTARY ANGLE  so 
the angle is =  180  - (5x-16 ) = 180-5x +16 =196 -5x ( angle in the triangke )

the other angle in the triangle = 50 ( alt interior angles line l parallel m 
then we took the triangle sum = 180

<span>196 -5x </span> + 2x +50 = 180     
so x = 22 
4 0
3 years ago
John's bedroom is shaped like a rectangle. The dimensions of the room are 10 feet by 14 feet. What is the best estimate of the l
natali 33 [55]

Answer:

c

Step-by-step explanation:

4 0
3 years ago
Need anyone’s help with this APEX question! Much appreciated!
VMariaS [17]

<u>Answer:</u>

The correct answer option is D. (x - 7) + 2.

<u>Step-by-step explanation:</u>

We are to determine whether which of the given options best describe the English expression:

<em>'two more than the quantity of a number minus seven'</em>

We can break this expression into smaller chunks to make it easier to translate.

1. two more than ---> +2

2. the quantity of a number ---> suppose the number to be 'x'

3. number minus 7 ---> (x - 7)

Combining these, we get (x - 7) + 2 so the correct answer option is D.

7 0
3 years ago
Read 2 more answers
The points shown on the graph represent the numbers in a geometric sequence.
sergejj [24]
D is the answer just took test
8 0
3 years ago
Read 2 more answers
(5w-2p)(3w+p-4) anyone one?
Elis [28]
The picture shows the answer
HOPE THIS HELPS!!

3 0
3 years ago
Other questions:
  • A piano manufacturer has a daily fixed cost of $1,800 and a marginal cost of $2,2000 per piano. Find the cost C(x) of manufactur
    5·1 answer
  • A scientist earning an annual salary of $49,839 gets a 4% raise. Estimate the new annual salary for this scientist.
    7·1 answer
  • How many different prisms can you make using 18 centimetre cubes?
    13·1 answer
  • Pleaasse explain:))))
    6·1 answer
  • CHOOSE ONLY 1 TO DO AND PLZ WRITE THE ANSWERS
    13·1 answer
  • So do you know ughhh
    10·1 answer
  • Yen paid $10.50 for 2.5 pounds of pretzels. What price did she pay for each pound of pretzels?
    15·2 answers
  • COME ON PLEASE HELP ME A FRICKING CRYING PLEASE HELP
    14·1 answer
  • Write each power as a product of the same factor then find the value of 10 power 6
    9·1 answer
  • Find the 2 angles coterminal to 1490 that have the smallest absolute value
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!