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
Jobisdone [24]
3 years ago
10

Find the first derivative of the function square root of x+1/4sin(2x)squared

Mathematics
1 answer:
gayaneshka [121]3 years ago
4 0
I'm thinking you want something that looks like this
\frac{dy}{dx}\sqrt{x+\frac{1}{4}sin^2(2x)} or it could be like this
\frac{dy}{dx}\sqrt{x}+\frac{1}{4}sin^2(2x)

use chain rule
dy/dx f(g(x))=f'(g(x))g'(x)
and √x=x^(1/2)
so
I'll do the first one first
\frac{dy}{dx}\sqrt{x+\frac{1}{4}sin^2(2x)}=
\frac{dy}{dx}(x+\frac{1}{4}sin^2(2x))^{\frac{1}{2}}=
\frac{1}{2(x+\frac{1}{4}sin^2(2x))^{\frac{1}{2}}}(1+sin(2x)cos(2x))=
\frac{1+sin(2x)cos(2x)}{2\sqrt{x+\frac{1}{4}sin^2(2x}}

the 2nd one is a bit simpler
\frac{dy}{dx}\sqrt{x}+\frac{1}{4}sin^2(2x)=
\frac{dy}{dx}x^{\frac{1}{2}}+\frac{1}{4}sin^2(2x)=
\frac{1}{2}x^{\frac{-1}{2}}+\frac{1}{4}sin^2(2x)=
\frac{1}{2x^{\frac{1}{2}}}+sin(2x)cos(2x)=
\frac{1}{2\sqrt{x}}+sin(2x)cos(2x)


in conclusion
\frac{dy}{dx}\sqrt{x+\frac{1}{4}sin^2(2x)}=\frac{1+sin(2x)cos(2x)}{2\sqrt{x+\frac{1}{4}sin^2(2x}} and
\frac{dy}{dx}\sqrt{x}+\frac{1}{4}sin^2(2x)=\frac{1}{2\sqrt{x}}+sin(2x)cos(2x)
depends which one it was
You might be interested in
Write and solve and equation to find how many movies they have time to show.
GalinKa [24]

Answer:

Equation 0.5 + 1.75(x) = 4

x = 2movies

Step-by-step explanation:

Given that,

movie night will last for 4 hours

each movie take 1.75 hours

time for eating popcorn 0.5 hours

To find,

number of movies which can be watched

<h2>Equation</h2><h2>0.5 + 1.75(x) = 4</h2><h2>Solve for x</h2><h3>1.75(x) = 4 - 0.5</h3><h3>1.75(x) = 3.5</h3><h3>x = 3.5/1.75</h3><h3>x = 2  </h3>

So, total number of movies which could be watched in 4hr = 2

<h3 /><h3 /><h3 /><h3 /><h3 /><h3 /><h3 />

7 0
3 years ago
I really need help what's the answer??
lys-0071 [83]
I think you just have to add all of the totals up??
5 0
3 years ago
Can someone help me with this please :)))
Inessa [10]
Answer : 58 square units.

Tip : break the shape down into shapes you can easily find the area of.

I found the area of the two squares on the bottom
They are identical and are both 2 units tall and two units long giving, giving an area of 4, and since there are two of them you can multiply the are by two giving you 8
Next found the area of the remaining shape which is just a rectangle that excludes the two bottom squares which is 10 units long and 5 units tall multiplying to 50
50+8=58
7 0
2 years ago
Read 2 more answers
Choose the solutions to the quadratic equation x2 – 8x – 9 = 0. –21 –1 9 29
8090 [49]

Answer:

-1 and 9

Step-by-step explanation:

To solve the quadratic, factor and set its factors equal to 0. Factoring is the action of breaking up a polynomial into pieces which multiply to make it. The factors are found by multiplying numbers to make C and add to B of ax^2+bx+c.

Here c = -9 and b = -8. The numbers -9 and 1 multiply to -9 and add to -8. These are the factors (x-9)(x+1).

Set each equal to 0 and solve for x.

x-9 = 0

x = 9

x+1 =0

x = -1

6 0
3 years ago
Please Help me! 20 points
malfutka [58]

Answer:

-9/4 ÷ (-2/3)

Step-by-step explanation:

-(2 1/4) ➡ -9/4

-2/3 ➡ (again a reciprocal needed) -3/2 since we need the result to be positive both expression should remain negative so the answer is -9/4 ÷ -2/3

6 0
3 years ago
Other questions:
  • Sam is 3 years younger than marco. marco is 15. how old is sam ? This is only 2 answer question
    6·2 answers
  • Find the total amount of interest earned on this savings account.
    11·2 answers
  • The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 44
    12·1 answer
  • What is the value of 3/7 times .1 divided by 5/21
    11·1 answer
  • Will mark brainliest
    9·2 answers
  • Solve this problem for y: 24=3y
    9·2 answers
  • Adjust quotients 32÷3,234
    15·1 answer
  • What is the equation of the line shown in the graph?
    15·1 answer
  • Please help me understand this equation
    6·1 answer
  • Written as a simplified polynomial in standard form, what is the result when (3x+6)^2
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!