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
Nastasia [14]
3 years ago
9

Derivative of sin3x using first principle

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
3 0

\displaystyle f(x)=\sin(3x)\\\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3(x+h))-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3x+3h)-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{3x+3h+3x}{2}\right)\sin\left(\dfrac{3x+3h-3x}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{\dfrac{3h}{2}}\cdot\dfrac{3}{2}

\displaystyle f'(x)=\lim_{h\to0}2\cos\left(\dfrac{6x+3h}{2}\right)\cdot\dfrac{3}{2}\\\\f'(x)=\lim_{h\to0}3\cos\left(\dfrac{6x+3h}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x+3\cdot 0}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x}{2}\right)\\\\f'(x)=3\cos(3x)

You might be interested in
6(x-2)=5x+3x+8 solve for x.
Mnenie [13.5K]

Answer:

x = -10

Step-by-step explanation:

 6 • (x - 2) -  (8x + 8)  = 0

Pulling out like terms :

3.1     Pull out like factors :

  -2x - 20  =   -2 • (x + 10)

Equation at the end of step  3  :

 -2 • (x + 10)  = 0

Equations which are never true :

4.1      Solve :    -2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.2      Solve  :    x+10 = 0

Subtract  10  from both sides of the equation :

                     x = -10

One solution was found :

                  x = -10

Processing ends successfully

plz mark me as brainliest :)

4 0
3 years ago
Read 2 more answers
Dolly gave Molly 6/8 packs of sweets. Molly had 18 packs of sweets. How many packs of sweets did Dolly start out with?
LenaWriter [7]
I think it is 22.5, since molly has 75% of the packs
6 0
3 years ago
Read 2 more answers
What is the value of x?
daser333 [38]

Answer:

x=22.5

Step-by-step explanation:

BM||DT

Using Intercept theorem/Intercept theorem

\frac{6}{6+15} =\frac{9}{9+x}

6(9+x)=9*21

54+6x=189

6x=135

x=22.5

At least I think so

4 0
4 years ago
Beth says that the graph of g(x) = + 1 is a translation of 5 units to the left and 1 unit up of f(x) = . She continues to explai
Nata [24]

Beth's description of the transformation is incorrect

<h3>Complete question</h3>

Beth says that the graph of g(x)=x-5+1 is a translation of 5 units to the left and 1 unit up of f(x) = x. She continues to explain that the point (0,0) on the square root function would be translated to the point (-5,1) on the graph of g(x). Is Beth's description of the transformation correct? Explain

<h3>How to determine the true statement?</h3>

The functions are given as:

g(x) = x - 5 + 1

f(x) = x

When the function f(x) is translated 5 units left, we have:

f(x + 5) = x + 5

When the above function is translated 1 unit up, we have:

f(x + 5) + 1 = x + 5 + 1

This means that the actual equation of g(x) should be

g(x) = x + 5 + 1

And not g(x) = x - 5 + 1

By comparison;

g(x) = x - 5 + 1 and g(x) = x + 5 + 1  are not the same

Hence, Beth's description of the transformation is incorrect

Read more about transformation at:

brainly.com/question/17121698

#SPJ1

7 0
2 years ago
What does B.O.D.M.A.S. or B.E.D.M.A.S. mean?
kakasveta [241]
B E D M A S  MEANS BRACKETS EXPONENTS DIVISION MULTIPLICATION ADDITION AND SUBTRACTION
8 0
4 years ago
Read 2 more answers
Other questions:
  • what is the probability of drawing 1 red marble and 3 blue marbles when given 10 red marbles and 7 blue marbles?
    5·1 answer
  • Which of the following are examples of inferential statistics?
    12·1 answer
  • Which two lines are parallel?
    10·2 answers
  • Which of the following is an inequality that represents the following scenario: Peter is at a local pizza shop. He wants to purc
    15·2 answers
  • 70,000 for 6 years at a simple interest rate of 10,5% find the interest paid on the loan an total paid
    12·1 answer
  • 4(3r+2)-7x i need help every answer i get is wrong.
    12·2 answers
  • PLEASE ANSWER ASAP!! GOOD 20 POINTS
    6·1 answer
  • Is y = 2(5)^x + 1 linear, exponential, or quadratic?
    5·1 answer
  • Solve each of the following equations show solution set on a number line 3x-1=8
    7·1 answer
  • PLEASE HELP
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!