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Calc 3 11.3

 

<== Calculus 3
Number Question Answer
See the work
1. Find the partial derivatives of the function

f(x,y) = rac{-2 x  + 4 y}{8 x + 7 y}

f_x(x,y) =
f_y(x,y) =


The work
2. Find the first partial derivatives of f(x, y) = sin(x - y) at the point (3, 3).

A. f_x(3, 3) =

B. f_y(3, 3) =

A) 1

B) -1
The work
3. Find the first partial derivatives of
\displaystyle f(x,y) = rac{2x - 2y}{2x +
2y} at the point (x,y) = (3, 4).

\displaystyle rac{\partial f}{\partial x}(3, 4) =

\displaystyle rac{\partial f}{\partial y}(3, 4) =

0.1633

-0.12245
The work
4. Find the partial derivatives of the function

w = \sqrt{6 r^2 + 5 s^2 + 9 t^2}

rac{\partial w}{\partial r} =
rac{\partial w}{\partial s} =
rac{\partial w}{\partial t} =




The work
5. Find the first partial derivatives of f(x,y,z) = z ( arctan(y/x) ) at the point (4, 4, 5).

A. rac{\partial f}{\partial x}(4, 4, 5) =

B. rac{\partial f}{\partial y}(4, 4, 5) =

C. rac{\partial f}{\partial z}(4, 4, 5) =

A) -5/8

B) 5/8

C) 0.7854
The work
6. The gas law for a fixed mass m of an ideal gas at absolute temperature T, pressure P, and volume V is PV = mRT, where R is the gas constant. Find the partial derivatives
\displaystyle rac{\partial P}{\partial V} =
\displaystyle rac{\partial V}{\partial T} =
\displaystyle rac{\partial T}{\partial P} =
\displaystyle rac{\partial P}{\partial V} rac{\partial V}{\partial T}rac{\partial T}{\partial P} =
-(mRT)/V^2

mR/P

V/(mR)

-1
The work
7. Find the partial derivatives of the function

f(x,y) = xye^{-8 y}
You should as a by product verify that the function f satisfies Clairaut's theorem.
f_x(x,y) =
f_y(x,y) =
f_{xy}(x,y) =
f_{yx}(x,y) =






The work
8. Find the partial derivatives of the function

f(x,y) = \int_y^x \cos(-1 t^2 + 8 t + 3)\, dt

f_x(x,y) =
f_y(x,y) =


The work