Discussion
If \( u = x^{2} + y^{2} \) with \( x = t \) and \( y = t^{2} \), then \( du/dt \) equals
Answer: C
The total derivative sums the two routes by which \( t \) reaches \( u \):
\[ \frac{du}{dt} \;=\; \frac{\partial u}{\partial x}\frac{dx}{dt} + \frac{\partial u}{\partial y}\frac{dy}{dt} \;=\; 2x(1) + 2y(2t). \]
Substituting \( x = t \) and \( y = t^{2} \) gives \( 2t + 4t^{3} \). Substituting first and then differentiating \( t^{2} + t^{4} \) confirms it
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