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
Angelina_Jolie [31]
4 years ago
14

Find dy/dx by implicit differentiation. y cos x = 5x2 + 3y2

Mathematics
1 answer:
lbvjy [14]4 years ago
5 0
Step 1:
Start by putting \frac{d}{dx} in front of each term

\frac{d}{dx}[y cos x]= \frac{d}{dx}[5x^2]+ \frac{d}{dx}[ 3y^2]
-----------------------------------------------------------------------------------------------------------------
Step 2:

Deal with the terms in 'x' and the constant terms
\frac{d}{dx}[ycosx]= 10x+ \frac{d}{dx} [3y^2]
----------------------------------------------------------------------------------------------------------------
Step 3:

Use the chain rule for the terms in 'y'
\frac{d}{dx}[ycosx]=10x+6y \frac{dy}{dx}
--------------------------------------------------------------------------------------------------------------
Step 4:

Use the product rule on the term in 'x' and 'y'
(y) \frac{d}{dx} cos x+(cos x) \frac{d}{dx}y =10x+6y \frac{dy}{dx}

y(-siny)+(cosx) \frac{dy}{dx} =10x+6y \frac{dy}{dx}
--------------------------------------------------------------------------------------------------------------

Step 5:

Rearrange to make \frac{dy}{dx} the subject
-y sin(y)+cos(x) \frac{dy}{dx} =10x+6y \frac{dy}{dx}
cos(x)  \frac{dy}{dx}-6y \frac{dy}{dx}=10x+y sin(y)
[cos(x) - 6y]  \frac{dy}{dx}=10x + y sin(y)
\frac{dy}{dx}= \frac{10x+ysin(y)}{cos(x)-6y} ⇒ Final Answer


You might be interested in
Which is an irrational number?
Solnce55 [7]
Sqrt(5/3)
and
sqrt(0/6)
many square roots are irrational numbers as long as they are not a perfect square
|-3| becomes positive 3
0.6 can be converted into a fraction 6/10
4 0
3 years ago
How do you learn math effectively?
Nataly [62]
That's such a broad question, and super subjective. I'd probably say that you learn math effectively from a good teacher or tutor, or if you're an individual learner, perhaps a textbook or any kind of online resource.
7 0
3 years ago
Read 2 more answers
Find the value of r (r,6) and (4,8) m=2
liubo4ka [24]
M is the slope, so, y=mx or y=2x. If y is 8 then x is 4.






y=6 x=r



6÷2=3, so r=3.

hope this helps and sorry if it got confusing.
6 0
4 years ago
Carlos purchased an antique chair at a
Arlecino [84]
If you know the answer, it is very easy to prove. You just have to do 27 - 15 = 12. Then, you do 12/15 is equal to 4/5, which is 80 percent. :)
4 0
3 years ago
What is the slope of the line?<br> 2x + 4y = 6x - y<br> Choose 1 answer:
Veseljchak [2.6K]

Answer:

slope is 4/5

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • If zb⊥ya , find m<br><br>A. 28<br><br>B.46<br><br>C.56<br><br>D.62<br><br>I'll give you brainliest
    6·1 answer
  • What is the constant of proportionality for the relationship shown in this table?
    7·1 answer
  • Multiply all whole numbers from 1 through 100, the largest power of 4 is a factor of the product of?
    11·1 answer
  • Can you help me solve this please
    14·1 answer
  • What is the equation of the ellipse with major vertices at (-6, 0) and (6, 0) and minor vertices at (0, 3) and (0, -3)?
    8·1 answer
  • The length of a rectangle is twice as long as the width. The area is 400 feet. Find the length and with of the rectangle.
    11·1 answer
  • What is the period? ​
    8·1 answer
  • It's not C, I took the test twice and C is wrong everytime.
    7·1 answer
  • What is 1/12 +2/3? Use the fraction strips to help you.help
    5·1 answer
  • What is the Scale Factor?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!