• Support PF! Buy your school textbooks, materials and every day products Here!

Partial derivative of tan(x + y)

  • #1

Homework Statement



[tex]f(x, y) = \tan(x + y) \\
f_x = ?
[/tex]



Homework Equations



[tex]\frac{dy}{dx}\tan(x)= \sec^2 x[/tex]

The Attempt at a Solution



I set y as constant, so I said derivative of y = 0 then took derivative of tan as above. However the answer should be
[tex]f_x = \sec^2(x + y)[/tex]

Why is y included?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
249
Hi username12345! :smile:
[tex]f(x, y) = \tan(x + y) \\
f_x = ?[/tex]

However the answer should be
[tex]f_x = \sec^2(x + y)[/tex]

Why is y included?
Because it's in g(x,y) in the chain rule … ∂f(g(x,y))/∂x = ∂f(g(x,y))/∂g ∂g(x,y))/∂x
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,794
925
The fact that the derivative of y is 0 does not mean that y itself is 0 and replacing tan(x+y) with tan(x) is saying y= 0.

What is the derivative of tan(x+ a) for constant a?
 
  • #4
What is the derivative of tan(x+ a) for constant a?
Well, what if you asked, what is derivative of [tex]tan(2x + a)[/tex]... I would say [tex]2 \sec^2(2x + a)[/tex]. So if that is correct then the derivative of [tex]\tan(x + a)[/tex] would be [tex]\sec^2(x + a)[/tex]. Is this correct?

Now considering the partial derivative with respect to x, we want y as a constant so replace a with y and we get [tex]f_x = \sec^2(x + y)[/tex]
 

Related Threads for: Partial derivative of tan(x + y)

  • Last Post
Replies
3
Views
21K
  • Last Post
Replies
5
Views
1K
Replies
10
Views
10K
Replies
2
Views
2K
Replies
0
Views
1K
Replies
2
Views
1K
  • Last Post
Replies
5
Views
4K
Top