× Didn't find what you were looking for? Ask a question
Top Posters
Since Sunday
a
5
k
5
c
5
B
5
l
5
C
4
s
4
a
4
t
4
i
4
r
4
r
4
Home Q & A Board Science-Related Homework Help Mathematics Calculus
New Topic  
bio_man bio_man
wrote...
solved
Administrator
Educator
Posts: 33241
Rep: 3442 15
5 years ago Edited: 4 years ago, duddy
\(x\cdot \sin y+y\cdot \cos x=0\)

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 423 times
1 Reply

Related Topics

Replies
wrote...
#1
Staff Member
4 years ago
👍
- Master of Science in Biology
- Bachelor of Science
New Topic      
Quick Reply
Explore
Post your homework questions and get free online help from our incredible volunteers
  1251 People Browsing
 120 Signed Up Today
Start New Topic Take the Tour CoursesNew Study Tools Topics Trending Browse by Textbook
Related Images
  
 162
  
 304
  
 299
Your Opinion
Who's your favorite biologist?
Votes: 586
Previous poll results: Who will win the 2024 president election?