Activity 11.4.3

If $f(x,y) = 3x^3 - 2x^2y^5$, find the partial derivatives $f_x$ and $f_y$.

If $f(x,y) = \displaystyle\frac{xy^2}{x+1}$, compute $\partial f/\partial x$ and $\partial f/\partial y$.

If $g(r,s) = rs\cos(r)$, find the partial derivatives $g_r$ and $g_s$.

Find all possible first-order partial derivatives of $q(x,t,z) = \displaystyle \frac{x2^tz^3}{1+x^2}.$