× Didn't find what you were looking for? Ask a question
  
  
  
  
Top Posters
Since Sunday
39
14
10
9
9
8
7
7
7
7
6
6
New Topic  
wrote...
Administrator
Educator
Posts: 24713
9 months ago


\(x\cdot \sin y+y\cdot \cos x=0\)

Rewrite with brackets for organization purposes:

\(\left(x\cdot \sin y\right)+\left(y\cdot \cos x\right)=0\)

Product rule twice, also differentiate implicitly with respect to \(x\):

\(\left(\sin y+x\cos y\ \frac{dy}{dx}\right)+\left(\frac{dy}{dx}\cos x-y\cdot \sin x\right)=0\)

Isolate for dy/dx:

\(\left(x\cos y\ \frac{dy}{dx}\right)+\left(\frac{dy}{dx}\cos x\right)=-\sin y+y\cdot \sin x\)

Factor out dy/dx on the left side:

\(\frac{dy}{dx}\left(x\cdot \cos y+\cos x\right)=-\sin y+y\cdot \sin x\)

Divide both sides by: \(\left(x\cdot \cos y+\cos x\right)\), giving us:

\(\frac{dy}{dx}=\frac{y\cdot \sin x-\sin y}{x\cdot \cos y+\cos x}\)
Read 240 times
The best way to say thank you is with a positive review:

  https://trustpilot.com/review/biology-forums.com 

Your support goes a long way!


Make a note request here
Related Topics
New Topic      
Hold tight!  A Bio Forums Expert has been contacted to start answering this thread.
Explore
Post your homework questions and get free online help from our incredible volunteers.
Learn More
Improve Grades
Help Others
Save Time
Accessible 24/7
  128 People Browsing
Your Opinion
Do you believe in global warming?
Votes: 182

Related Images
 193
 96
 60

▶️ Video: Adolescent Diabetes

For a complete list of videos, visit our video library