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]
3 years ago
14

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

Mathematics
1 answer:
lbvjy [14]3 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
Can someone help me find X of this triangle? thanks :)
tino4ka555 [31]

Since it is an equilateral triangle, all of the sides are the same length.

So, x=14 :)

Hope this helps!

7 0
2 years ago
Read 2 more answers
Delia drove 290 miles in 5 hours. At this rate, how far will she drive in 7.5 hours?
HACTEHA [7]

Answer:

464

Step-by-step explanation:

5 0
2 years ago
The game of Scrabble has 100 tiles. The diagram shows the number of tiles for each letter and the​ letter's point value. One til
egoroff_w [7]

Answer:

10%

Step-by-step explanation:

In the image attached below, we can see that there are

8 tiles of letter O

2 tiles of letter V

This means that there are 10 total tiles of the letters that you want to get (O and V). Since there are a total of 100 tiles we need to divide this value by 100 to get the probability of getting one of these tiles.

10 / 100 = 0.10 or 10%

Finally, we can see that the probability of selecting a O or a V is 10%

7 0
2 years ago
Uncle percy only has 10% of teashirts he started with if he has 25 now how many did he start with
nataly862011 [7]

Answer:

250

Step-by-step explanation:

Since you are looking for the amount of shirts he had you will need to divide 25 by .10 or just multiply by 10.

6 0
3 years ago
Read 2 more answers
THESE are PSAT questions please help.​
cricket20 [7]

Answer:

Ok so number 7 is x>4

Number 6 is b

Number 5 is correct

Idk the other one

❤️❤️❤️Hope This Helps❤️❤️❤️

3 0
3 years ago
Other questions:
  • The problem is: 2x-2(x-2y)+1/4(4x-12y)
    12·1 answer
  • A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess
    5·1 answer
  • It say to state weather each figure is a polyhedron
    5·1 answer
  • Rewrite the following equation in slope intercept form<br><br> 14x+13y=12
    7·1 answer
  • What is the coefficient of the term 4/3yz
    7·1 answer
  • 2 3 5 9 17 _ what is the next number in the sequence
    12·1 answer
  • Which of the following graphs represents a one-to-one function?
    15·2 answers
  • a study done by researchers at a university concluded that 70% of all student athletes in this country have been subjected to so
    11·1 answer
  • Which list of ordered pairs does NOT represent a function? A.(8, 80), (6, 80), (3, 80), (7, 80), (5, 80) B. (7, 80), (6, 60), (5
    7·1 answer
  • Please helppp me!!!!!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!