If $f(x,y)=sin(\frac{6x}{1y}),$ calculate $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}$ and $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}$

Solution

Using the chain rule for functions of one variable, we have

$\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}=(,)*\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}(\frac{6x}{1y})$

$=$

$\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}=(,)*\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{y}}(\frac{6x}{1y})$