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Activity 11.3.3.
(a)
If
\(f(x,y) = 3x^3 - 2x^2y^5\text{,}\) find the partial derivatives
\(f_x\) and
\(f_y\text{.}\)
(b)
If
\(f(x,y) = \displaystyle\frac{xy^2}{x+1}\text{,}\) compute
\(\partial f/\partial x\) and
\(\partial f/\partial y\text{.}\)
(c)
If
\(g(r,s) = rs\cos(r)\text{,}\) find the partial derivatives
\(g_r\) and
\(g_s\text{.}\)
(d)
Find all possible first-order partial derivatives of
\(q(x,t,z) = \displaystyle \frac{x2^tz^3}{1+x^2}.\)
