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
Joelle would like to tip her hairdresser 20%. If her haircut was $38.00, which expression should she use to find the tip amount?
Vilka [71]
I pretty sure you would use x over 38.00 = 20 over 100 then cross multiply them
6 0
3 years ago
Change 1/7 / 4/21 to a ratio?<br>​
sergeinik [125]

Answer:

3:4

Step-by-step explanation:

(1/7)/(4/21) = (1/7)×(21/4) = 3/4 = 3:4

6 0
2 years ago
Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
Tcecarenko [31]

Answer:

The slope of f(x) is equal to the slope of g(x).

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

step 1

Find the slope of the function f(x)

we have the points

(0,-1) and (3,1)

substitute in the formula

m=\frac{1+1}{3-0}

m_1=\frac{2}{3}

step 2

Find the slope of the function g(x)

take two points of the given table

(0,2) and (3,4)

substitute in the formula

m=\frac{4-2}{3-0}

m_2=\frac{2}{3}

step 3

Compare the slopes

m_1=m_2

therefore

The slope of f(x) is equal to the slope of g(x).

7 0
3 years ago
Read 2 more answers
Fuimos al Circo "Hermanos Poncho y Carlos", y tuvimos que pagar en total $350 por mis dos hermanos, mis padres y yo. Mi mamá pag
nalin [4]

Answer:

$160

Step-by-step explanation:

El monto total a pagar es de $350

\dfrac{1}{7} es pagado por mamá

\dfrac{2}{5} es pagado por el hermano mayor

La porción pagada por papá es

1-(\dfrac{1}{7}+\dfrac{2}{5})=1-(\dfrac{5+14}{35})\\ =1-\dfrac{19}{35}\\ =\dfrac{35-19}{35}\\ =\dfrac{16}{35}

Esta cantidad pagada por papá es

350\times\dfrac{16}{35}\\ =10\times 16\\ =\$160

Esta cantidad pagada por papá es $160.

3 0
2 years ago
It would be great if someone could help me with this problem
GaryK [48]
Y-intercept (0, 1)
Equation of asymptote y=0

Equation of asymptote can also be called horizontal asymptote.
It means the place where the line almost meets but actually not touching the place. The line almost touches y=0 but it actually does not touch it.

7 0
3 years ago
Other questions:
  • NEED HELP ASAP !!! Please
    9·1 answer
  • PLZ HURRY!!! WILL MARK BRAINLIEST!!!! For several months, an ice-cream vendor collects data showing the number of cones sold in
    15·2 answers
  • How to subtract this question 91.49-0.7
    11·2 answers
  • The vertices of ΔABC are (-2,0), (-2, 3), and (-5, 1). T(x,y) = (x + 1, 3y) represents the transformation of the triangle. What
    6·2 answers
  • Jacadi is setting up a tent. Each section of a tent pole is
    11·1 answer
  • Penny is training for a race. First she ran 1/10 of a mile 4 times. Next she ran 1/5 of a mile 3 times. Then she ran 3/10 of a m
    9·2 answers
  • Re-write 15/9 as a mixed number
    12·1 answer
  • Please answer right its very important!
    13·2 answers
  • Solve the inequality 2(x-3)-5x&lt;9
    11·2 answers
  • When three or more points lie on the same straight line.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!