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
malfutka [58]
3 years ago
6

Differentiate with respect to X

%7D%20" id="TexFormula1" title=" \sqrt{ \frac{cos2x}{1 +sin2x } } " alt=" \sqrt{ \frac{cos2x}{1 +sin2x } } " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Mice21 [21]3 years ago
5 0

Power and chain rule (where the power rule kicks in because \sqrt x=x^{1/2}):

\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'

Simplify the leading term as

\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}

Quotient rule:

\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}

Chain rule:

(\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)

(1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)

Put everything together and simplify:

\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}

=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}

=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}

=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}

=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}

=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}

=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}

You might be interested in
What is the recursive formula for the sequence? -14, -8, -2, 4, 10,...
FinnZ [79.3K]
You are adding 6 to each number. (N-1)+6, I guess
3 0
3 years ago
ALGEBRA 1, SEM. 2
grigory [225]
2•(1/4)^(2-1)= 2•(1/4)= 1/2
2•(1/4)^(3-1)= 2• (1/4)^2 = 2•1/16=1/8
3 0
3 years ago
Hello it's mathhhhhh
yaroslaw [1]

Answer:

36

Step-by-step explanation:

4*6=24

3*4=12

24+12=36

8 0
3 years ago
Read 2 more answers
Please Help!
vovikov84 [41]

Answer:

8

Step-by-step explanation:

We can use triangle inequality, let AC = x:

x+4 > 5

x+5 > 4

9 > x

Simplifying:

x>1

x>-1

9>x

Thus: 9>x>1

So the Largest whole number is 8

3 0
3 years ago
WILL MARK BRAINLIST!!!!
Lesechka [4]

Answer:

Step-by-step explanation:

I had this answer

8 0
3 years ago
Read 2 more answers
Other questions:
  • In adding 4/5 + 18/100 the least common denominator is:
    6·1 answer
  • Solve for x y=3mx-7b
    14·1 answer
  • 8 customers entered a store over the course of 10 minutes.
    7·1 answer
  • HELP PLS i need this right now
    8·1 answer
  • What do you need to do to extend a number pattern
    8·1 answer
  • 1. Find the circumference radius of 14 a. Give an exact answer in terms of . (1 point) b. Use ≈ 22/7 and express your answer as
    10·1 answer
  • The length of a rectangle is 5ft longer than twice the width. if the perimeter is 70 ft. find the length and width of the rectan
    8·1 answer
  • if I Owen 0.0186753 of a Bitcoin. if bit coin goes up $1000 from $50000 . how much would my Bitcoin gain in dollars? ​
    12·2 answers
  • Can someone please help me please
    7·1 answer
  • What is a computer ​
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!