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
dmitriy555 [2]
2 years ago
9

Derivative by first principle logsecx²​

Mathematics
1 answer:
Maru [420]2 years ago
5 0

Answer:

\displaystyle \frac{d}{dx}[\log \big( \sec (x^2) \big)] = \frac{2x \tan x^2}{\ln 10}

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

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

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle y = \log \big( \sec (x^2) \big)

<u>Step 2: Differentiate</u>

  1. Logarithmic Differentiation [Derivative Rule - Chain Rule]:                      \displaystyle y' = \frac{(\sec x^2)'}{\ln (10) \sec x^2}
  2. Trigonometric Differentiation [Derivative Rule - Chain Rule]:                   \displaystyle y' = \frac{\sec x^2 \tan x^2 (x^2)'}{\ln (10) \sec x^2}
  3. Simplify:                                                                                                         \displaystyle y' = \frac{\tan x^2 (x^2)'}{\ln 10}
  4. Basic Power Rule:                                                                                        \displaystyle y' = \frac{2x \tan x^2}{\ln 10}

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

Unit: Differentiation

You might be interested in
A book designer decided that the pages of a book should have 1-in. margins at the top and bottom and 1 2 in. margins on the side
alexgriva [62]

Answer:

A = 54.8 - (1200/x) - 2x

Step-by-step explanation:

Given <em>x</em> the wide and <em>y</em> the height, we have

x*y = 50

⇒  y = 50/x

The area of the printed region is A = w*h

where

Wide: w = (x-2*1.2) = x-2.4

Height: h= (y-2*1) = y-2

then

A = (x-2.4)(y-2) = xy - 2.4y - 2x + 4.8 = 50 - 24*(50/x) - 2x + 4.8

⇒  A = 54.8 - (1200/x) - 2x

5 0
3 years ago
K + 12 ≥20, if k = 15 <br> HELP PLEASE!!
Andrei [34K]

Answer:

Step-by-step explanation:

k= 15

k+12 ≥ 20

15+12 ≥20

27 ≥ 20 True

4 0
2 years ago
Dierdre’s work to solve a math problem is shown below.
kramer

Step-by-step explanation:

step 1

6 0
3 years ago
Read 2 more answers
Which set of data has the weakest linear association?
motikmotik
The top left-hand corner set of data has the weakest linear association.

Hope that helped!!! :)
5 0
3 years ago
Please help me with this​
levacccp [35]

Answer:

They weigh 1/6

Step-by-step explanation:

So what you do is Divide 1/4 bye 1 1/2 so that you can figure out how much 1 1/2 bags weigh and that equals 1/6

8 0
3 years ago
Other questions:
  • How much would 1 espresso cost?
    7·1 answer
  • G(n) = 3n - 3<br>f(n) = 2n - 4<br>Find g(-3) f(-3)​
    5·1 answer
  • Simplify the expression below.<br> 9x + 10 - 2x + 1
    7·2 answers
  • What is the distance between the points (5, -1) and (5,<br> 3)
    13·1 answer
  • What is the slope and y intercept
    10·1 answer
  • Write an exponential function in the form y=ab^(x) that goes through points (0,4) and (6, 2916)
    12·1 answer
  • What is the measure of arc WYZ?
    10·2 answers
  • a storm blew down many trees. several neighbors rented a chain saw for $232.85 and helped each other cut up and stack wood. the
    13·2 answers
  • Who wants 40 points ?? answer this
    15·2 answers
  • How many workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!