# Math Help - Partial Derivatives

1. ## Partial Derivatives

Suppose f is a differentiable function of x and y, and g(u,v)=f(e^u+sinv, e^u+cosv) use the table of values to calculate gu(0,0) and gv(0,0).

at (0,0) f=3, g=6 fx=4 fx=8

I have no clue how to do this someone please help

2. Originally Posted by multivariablecalc
Suppose f is a differentiable function of x and y, and g(u,v)=f(e^u+sinv, e^u+cosv) use the table of values to calculate gu(0,0) and gv(0,0).

at (0,0) f=3, g=6 fx=4 fx=8

I have no clue how to do this someone please help
Let $x = e^u+\sin v$ and $y = e^u+\cos v$ so

$
g_u = f_x x_u + f_y y_u = e^u f_x + e^u f_y
$

$
g_v = f_x x_v + f_y y_v = \cos v f_x - \sin v f_y
$

Do you have a table of values for $f_x(1,2)$ and $f_y(1,2)$?

3. If the problem say "use the table of values" you had better have a table of values! Please post the entire problem, including the table of values.

4. fx(1,2)=2, fy(1,2)=5, f(0,0)=3, f(1,2)=6, g(0,0)=6, g(1,2)=3, fx(0,0)=4,fy(0,0)=8

5. Welcome back! Do you see why you needed to know fx(1,2) and fy(1,2)?

6. Well I am not the same person who posted this thread. However, assuming this person was referring to problem #11 of section 11.5 of Essential Calculus-Early Transcendentals (James Stewart), then these are the correct values. If I am not mistaken, gu(0,0)=fx(1,2)e^u +fy(1,2)e^u =2e^0 +5e^0=7. gv(0,0) is not much different.

7. Oh, I see! (Although if you had gone on a 4-month quest for the table of values perhaps you would have have returned a different person!)

I don't think you're mistaken. Hopefully you can also see how Danny was holding one variable constant while differentiating with respect to the other.