Saturday

August 30, 2014

August 30, 2014

Posted by **mark** on Sunday, October 5, 2008 at 3:52pm.

Obtain expressions for Zx and Zy in terms of fu and fv.

I don't understand the "in terms of" part. How do I do this question? thank you

- Calculus-partial derivatives -
**Count Iblis**, Sunday, October 5, 2008 at 8:35pmdZ = Zx dx + Zy dy (1)

Also:

dZ = df = fu du + fv dv (2)

Express du and dv in terms of dx and dy:

du = ux dx + uy dy (3)

dv = vx dx + vy dy (4)

Substitute (3) and (4) in (2):

dZ = fu (ux dx + uy dy ) + fv (vx dx + vy dy) =

(fu ux + fv vx) dx + (fu uy + fv vy)dy

Comparing this to (1) then gives:

Zx = fu ux + fv vx

Zy = fu uy + fv vy

**Related Questions**

calculus - find the second-order partial derivatives of f(x,y)=x^3 + x^2y^2 + y^...

calculus - Just doing example questions to better understand. Find all first and...

calculus - a)find the first partial derivatives of f(x y)= x √1+y^2 b)find...

Math(Please help) - Evaluate: f(x,y)=2x^3e^y a) partial derivative with respect ...

Calculus - Find all first partial derivatives: f(x,y)=e^(xy)cosx

calculus - find the partial derivatives du/dx, du/dy and du/dt. u= root (r^2+s^2...

Calculus - HELP plz! - Find all of the first partial derivatives of f(x,y,z)=...

Calculus: Derivatives - I'm having trouble understanding what derivatives in ...

Calculus (Partial Fractions) - My Calculus class just started Partial Fractions...

Math - Calculus - Im trying to understand related rates here and im getting ...