Partial Derivatives

1. Oct 7, 2004

Spectre32

Partial Derivatives of this(respect to x,y).

Code (Text):
Z = (x+y) Sec(xy).
Would my first move be to multiply the
Code (Text):
(x+y)
tot he other side? If so I'm algerba is a bit sketchy :uhh: , how would it be done.

2. Oct 7, 2004

faust9

You can algebraically expand the quantity (x+y), or you can use the product rule for derivatives. Either method will get you the result. I'd keep it the way it is personally because if you expand the quantity you'll have to use the product rule twice.

Good luck.

3. Oct 7, 2004

Spectre32

Ok so would I get something like this:

[(x+y)+((sin(xy)*y)/(cos(xy)^2))] - [(1+y)+sec(xy)] ??

4. Oct 7, 2004

faust9

No, how did you get that? Laptop battery almost dead so I'll not respond to this until later tonight BTW. When doing a partial w/ respect to x, y becomes a constant and vice versa.

Do this: (x+1)sec ((1)(x))d/dx

What would that look like?

5. Oct 7, 2004

Spectre32

(cos(x) * (x+1)*sin(x))/(Cos(x)^2)

6. Oct 7, 2004

Spectre32

Whoops.... Now I see what I did wrong... wow i'm retarded. I forgot to go through and Differentate Y and then figure it out. But I still think I did it wrong. Sec[x] + (1 + x) Sec[x] Tan[x]

Last edited: Oct 7, 2004