4. [6 pts] Compute $\frac{\partial f}{\partial u}|_P$ if $f(x, y) = x^2 y^3$, $x = u^2 - v^2$, $y = 2uv$, $P = (\sqrt{8}, \sqrt{2})$. Simplify.
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Let's solve the second equation for v: v = 1/u Substituting this into the first equation, we get: 8 = u^2 - (1/u)^2 Simplifying this equation, we get: 8 = u^2 - 1/u^2 Multiplying both sides by u^2, we get: 8u^2 = u^4 - 1 Rearranging the equation, we get: u^4 - Show moreβ¦
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