$\newcommand{\ds}{\displaystyle}$ $\newcommand{\ve}[1]{\overrightarrow{\mathbf{#1}}}$ $\newcommand{\ora}{\overrightarrow}$ $\newcommand{\com}[1]{\left\langle #1 \right\rangle}$ $\newcommand{\mb}{\mathbf}$ $\newcommand{\ivec}{\hat{\mbox{\bf{\dotlessi}}}}$ $\newcommand{\jvec}{\hat{\mbox{\bf{\dotlessj}}}}$ $\newcommand{\kvec}{\hat{\mbox{\bf{k}}}}$ $\newcommand{\magn}[1]{\left|\left| #1 \right|\right|}$ $\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}$

Partial Derivatives

Click on each problem to expand and view the problem. You can then download a solution to the problem in PDF format. You can collapse the problem by clicking on the problem again.

• 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