A community for students.
Here's the question you clicked on:
 0 viewing
Babyslapmafro
 2 years ago
Please help. How do you find the partial derivative of arctan(x/y) with respect to x?
Babyslapmafro
 2 years ago
Please help. How do you find the partial derivative of arctan(x/y) with respect to x?

This Question is Closed

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1do you know the meaning of partial derivative ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1then have you tried to find the partial derivative ? where r u stuck ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1do you know derivative of inverse tan function ?

Babyslapmafro
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ 1 }{ x ^{2}+1 }\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1good! now since 'y' is constant, its like taking derivative of inverse tan (ax) {where 'a' =1/y} so, apply the chain rule (know it?) \([\tan^{1}{ax}]'= \dfrac{1}{1+(ax)^2}\dfrac{d}{dx}(ax)=....?\)

Babyslapmafro
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ 1 }{ 1+(\frac{ 1 }{ y ^{2} }+\frac{ 2 }{ y }x+x ^{2} )}\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1where does the expression 1/y^2 +2y/x +x^2 come from ???

Babyslapmafro
 2 years ago
Best ResponseYou've already chosen the best response.1i replaced a with 1/y

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1right, so, it was not (a+x)^2 , it was (ax)^2 so, the denominator would just be \(1+x^2/y^2\) got this ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1what about the numerator ?? d/dx (ax) =...?

Babyslapmafro
 2 years ago
Best ResponseYou've already chosen the best response.1numerator = (1/y)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1no....in chain rule, we need to take derivative of the inner function (here ax or x/y) which is, as you correctly said, 1/y :)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1one last step of simplification : \(\dfrac{1/y}{1+x^2/y^2}=....?\) multiply numerator and denominator by y^2 to simplify this :)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1remember that the numerator was 1/y and y^2/y would just be 'y' so your final answer would look like this : \(\large \dfrac{y}{x^2+y^2}\)

Babyslapmafro
 2 years ago
Best ResponseYou've already chosen the best response.1oh right ya, thanks
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.