In-class work for 20 June 2012
1.) Compute all first partial derivatives of the function $f(x,y) =...$

    a.) $x^2y^2+y^3+3xy$

    b.) $\sin(x) \sin(y)$

    c.) $\log(xy)\sin(y^2)$

    d.) $\frac{1}{x} \sin(xy)$

    e.) $\log(\cos(xy)) - \log \left( \dfrac{1}{\sec(xy)} \right)$

    f.) $\cos(xy) \sqrt{\displaystyle\int_0^x \sin(t) dt})$

2.) Compute all second partial derivatives of the function $f(x,y) =...$

    a.) $x^2+3xy$

    b.) $\log(y \sin(x))$

    c.) $\log(\sin(xy))$

    d.) $\cos(x) \tan(x)$

3.) If $u = x^3yz^4$, compute...

    a.) $\frac{\partial u}{\partial x}$

    b.) $\frac{\partial^2u}{\partial x \partial y}$

    c.) $\frac{\partial^3u}{\partial x^2 \partial z}$

    d.) $\frac{\partial u}{\partial w}$

    e.) $\frac{\partial^4 u}{\partial x^3 \partial y}$