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