
Partial Derivatives

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• Exam 1, Spring 2001, Problem 4

• Exam 1, Fall 2005, Problem 6

• Exam 1, Practice Fall 2009, Problem 9

• Exam 1, Practice Fall 2009, Problem 10

• Exam 1, Spring 2010, Problem 2a

• Exam 1, Spring 2010, Problem 2b

• Exam 1, Fall 2011, Problem 3

Let $f(x,y,z)=\sqrt{xy+2xz+3yz}$.

(a) Find $\ds\pd{f}{x}$, $\ds\pd{f}{y}$, and $\ds\pd{f}{z}$.

(b) Let $x=uv$, $y=u+2v$, and $z=-v^2$. Compute $\ds\pd{f}{u}$ when $u=2$ and $v=-1$.

• Exam 1, Spring 2012, Problem 4

Let $f(x,y)=\ln(x^2+y^2-16)$.

(a) Sketch the domain of $f$.

(b) Compute the partial derivatives $f_x$, $f_y$, and $f_{xx}$.

• Exam 1, Spring 2013, Problem 5

Compute the first partial derivatives of the function $\ds f(x,y)=\frac{y}{3x^2+4y^2}$.

• Final Exam, Practice Fall 2009, Problem 9

• Final Exam, Spring 2010, Problem 2

• Fainl Exam, Fall 2010, Problem 9