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
Reena scored 25 marks out of 30 in Math test and 35 out of 42 in Science test. In which test has she scored better?
alexandr402 [8]

Step-by-step explanation:

None is better they have the same score in percentage.

5 0
3 years ago
Read 2 more answers
When testing for differences between treatment means, a confidence interval is computed with __________________?
KIM [24]
The confidence interval is based on mean square error. T<span>he </span>mean squared error<span> (</span>MSE<span>) </span><span>of an </span>estimator<span> measures the </span>average<span> of the squares of the </span>errors<span> or </span>deviations.<span> MSE is calculated by the formula attached in the picture, where Xbar is a vector of predictions, X is the vector of predicted values. </span>

5 0
3 years ago
Pablo mixes three units white paint and one unit of black paint to make gray paint. What two equations show the relationship bet
svet-max [94.6K]
It’s b and when you put w to egbert
8 0
3 years ago
Nolan used the following procedure to find an estimate for StartRoot 18 EndRoot.
stiks02 [169]

Answer:

Nolan correctly identified the square  numbers before and after 18.

The square roots of them are 4 and 5.

Clearly, square root of 18 should lie between 4 and 5 only.

He, then carefully squared 4.1, 4.2, 4.3 etc. and identified that 4.3 squared is nearer to 18.

Since, Nolan is finding estimated square root, his steps are cool and he didn't make any error.

4 0
3 years ago
Read 2 more answers
Add (3+2i)+(-5+6i)<br> A) -8+8i<br> B) -8-4i<br> C) -2+8i<br> D) -2+4i
balandron [24]
The answer it b your welcome
6 0
3 years ago
Read 2 more answers
Other questions:
  • 5n(3n-n+8) slove it please
    11·1 answer
  • Victor runs 3 laps around the track every 5 minutes. How many laps does Victor run in 1 minute?
    12·1 answer
  • A ball is dropped from a height of 12 feet and returns to a height that is 1/2 of the height from which it fell. The ball contin
    12·2 answers
  • 52 rounded to the nearest ten
    5·2 answers
  • 40 point.!!!! HELP ME PLEASE MY MOM GONNA YELL AT ME
    8·1 answer
  • Trapezoid PSTK is isosceles. SK = 20, SH = 12, If ST = 1 4 HK, find HK, Area of PTSK, m∠P, and PS.
    14·1 answer
  • Simplify the following expression. 3 + [(7 ÷ 7)] × 6
    6·2 answers
  • PLEASE HELP ME!!!!!!!!!! MUST SHOW ALL WORK
    5·1 answer
  • Helpppp hurry and no links please
    9·1 answer
  • Solve 3a<br> 17<br> 7<br> 8<br> 9<br> - (2² + 1)² + a<br> when a = 8
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!