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
mr Goodwill [35]
3 years ago
5

Finding Derivatives Implicity In Exercise,Find dy/dx implicity. xey - 10x + 3y = 0

Mathematics
1 answer:
uranmaximum [27]3 years ago
5 0

Answer:

\dfrac{dy}{dx}=\dfrac{10-e^y}{(xe^y+3)}

Step-by-step explanation:

Given:

The implicit equation is given as:

xe^y-10x+3y=0

In implicit differentiation, we treat 'y' as a function of 'x' and differentiate both sides of the equation with respect to 'x' and then collect all the \frac{dy}{dx} together and finally solve for \frac{dy}{dx}.

So, differentiating both sides of the above equation with respect to 'x'. This gives,

\frac{d}{dx}(xe^y-10x+3y)=\frac{d}{dx}(0)\\\\\frac{d}{dx}(xe^y)+\frac{d}{dx}(-10x)+\frac{d}{dx}(3y)=0\\\\\textrm{Using product rule, (uv)' = uv' + vu'}\\\\(x\cdot e^y\cdot \frac{dy}{dx}+e^y\cdot 1)-10\cdot1+3\frac{dy}{dx}=0\\\\\frac{dy}{dx}(xe^y)+e^y-10+\frac{dy}{dx}(3)=0\\\\\textrm{Grouping}\ \frac{dy}{dx}\textrm{ terms together}\\\\\frac{dy}{dx}(xe^y+3)+e^y-10=0\\\\\frac{dy}{dx}(xe^y+3)=10-e^y\\\\\dfrac{dy}{dx}=\dfrac{10-e^y}{(xe^y+3)}

Therefore, the derivative \frac{dy}{dx} implicitly is:

\dfrac{dy}{dx}=\dfrac{10-e^y}{(xe^y+3)}

You might be interested in
What is 6 divided by 2
Pani-rosa [81]
Answer: 3
To check:
2 * 3 = 6
7 0
3 years ago
Read 2 more answers
Charlie is flying a kite one afternoon and steps on the end of the string to have his
Butoxors [25]

Answer:

roubd it to 20 and you will get 679.90

7 0
3 years ago
Solving multi-step <br> 2(8+4c)=32 <br>c=​
professor190 [17]
You’re gonna multiplying & you do that it would be 16+ 8c= 32 and then you subtract 16 from 32 and that gives you 8c = 16 and you dived and C = 2
7 0
3 years ago
ASAP!<br> lines p and q are parallel what is the sum of the degrees measure of angles x and y
blagie [28]
90? there’s a 45 degree angle at the bottom left and it looks like the same angle as x and y
7 0
2 years ago
Please help me! i really need help​
deff fn [24]

Answer:

24.3

Step-by-step explanation:

because each side is the same. one has 12 inch and the other is 9. So you subtract 9 from 12 and get 3. Then you have to find out what the other mesurment is for the bigger shape, which is 2.7 because 32/12=2.66666, so u round and get 2.7 . so theen you multiply 9 and 2.7 and get 24.3! Hope this helps.

7 0
3 years ago
Other questions:
  • Find the quotient 27 divided by 623.
    12·1 answer
  • What is the value of the expression when n=3?​
    12·2 answers
  • Given a random sample of 85 people attending a workshop, 63 of the respondents said the workshop was useful. What is the sample
    7·2 answers
  • Express the decimal 0.907 as a percent?
    5·2 answers
  • 2y+5y-3yTo the second power
    6·2 answers
  • Do (12+6)÷2 and 12+6÷2 have the same answer? Explain why.
    14·2 answers
  • Can someone answer this question
    10·2 answers
  • An electronics company has two production facilities, denoted A and B. During an average week, facility A produces 2000 computer
    6·1 answer
  • What is the point slope form of (1,3) , (-1,4)​
    11·1 answer
  • Today is the birthday of Rahul and he is 3 times
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!