Problem $10$ is an algebra$/$limit problem which llustrates the power rule of derivatives being "derived" from the limit process. Most of you can see the answers without doing the algebra$/$limit process. I would like you to show the work that gives the answers without using the power rule. It is nice to give credit to those brilliant mathematicians $($Newton and Leibniz$)$ who developed calculus. The concept of limits has been around for over $2000$ years but derivatives were developed in $1700.$

Given $f(x,y)=x^2{y}^2$ use Algebra to find

a$)\underset{x0}{lim}\frac{f(xx,y)-f(x,y)}{x}$

b$)\underset{y0}{lim}\frac{f(x,yy)-f(x,y)}{y}$