Partial Derivatives

Show all your work $to$ support your answers.

Find the partial derivatives $f_x$ and $f_y$ for the function: $f(x,y)=x{e}^y$

Find the partial derivatives $\frac{\text{d}\text{e}\text{l}\text{x}}{\text{d}\text{e}\text{l}\text{x}}$ and $\frac{\text{d}\text{e}\text{l}\text{x}}{\text{d}\text{e}\text{l}\text{y}}$ for the function:

$z=y^{z}sin(4x)$

Find the fours second partial derivatives for the function:

$f(x,y)=2x^2{y}^2+x^{2}y$

Find the first partial derivatives for the function:

$f(w,x,y,z)=w^{2}x{y}^2+x{y}^2{z}^2$

The Body mass index $(BMI)$ for $an$ adult human $is$ given $by$ the

function $B=\frac{w}{h^2},$ where $wB=703\frac{w}{h^2}h,is$ the BMI $an$ increasing $or$ decreasing function $of$

$w?$

$c.$ Find the rate $of$ change $of$ the BMI with respect $to$ height $ata$

constant weight.

$b.$ For fixed $w,is$ the BMI $an$ increasing $or$ decreasing function $of$

$h?$