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
Each of students reported the number of movies they saw in the past year. Here is what they reported. 6, 13, 13, 19, 16, 4, 5 Fi
Artemon [7]

Answer:10.9

Step-by-step explanation:You add all of the numbers together (76) and then divide by the total of numbers (7). You will get 10.85714286, you have to round to the nearest 10th , so the 5 changes the 8 to a 9.

3 0
3 years ago
The slope of the line below is 2. Which of the following is the the point-slope form of the line?
Jobisdone [24]

Answer:  y + 1 = 2 (x -1)

Step-by-step explanation:

Point slope form is:

y - y1 = m (x - x1)

Point on the line is (1, -1) and slope is 2

m = 2

y1 = -1

x1 = 1

y - (-1) = 2 (x - 1) or y + 1 = 2 (x -1)

5 0
3 years ago
What is the 20th term to -30,-22,-14,-6?
galben [10]
98.
The numbers increase by intervals of 8. You need 16 more terms until you reach the 20th term, so 16*8=128.
128-30=98.
5 0
3 years ago
What is 9 times 199 in distributive property
Mrrafil [7]

Answer:

1791

Step-by-step explanation:

6 0
3 years ago
Answer ASAP PLS
Ipatiy [6.2K]
The answer is 1, just use a calculator.
7 0
3 years ago
Other questions:
  • What is the average rate of change from x= -1 to x = 1 ?
    15·2 answers
  • s=p-0.15p represents the sale price s of an item with an original price p, after a 15% discount. Make a table to find the discou
    12·1 answer
  • A keep tossing a fair coin, until he get 2 consecutive heads, define x to be the number of tosses for this process; b keep tossi
    9·1 answer
  • How much would $200 invested at 6% interest compounded annually be worth after 5 years? Round your answer to the nearest cent. A
    10·1 answer
  • Solve for x : 5x-9=7x+6-2x
    5·2 answers
  • Find the common ratio 24,18,37/2,81/8
    12·1 answer
  • WILL MARK BRAINLEST!!!!!!!
    13·1 answer
  • What is the correct answer?​
    11·2 answers
  • 6) find HJ<br> 8)find IK
    5·1 answer
  • HELP PLEASE
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!