Allied & ICAR Exam Bank • ALLIED_2644 NAT • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Total differentiation

Question Statement:

If $w = f(u, v)$ where $u = x - y$ and $v = x + y$, then $\frac{\partial w}{\partial x} + \frac{\partial w}{\partial y}$ in terms of $\frac{\partial w}{\partial v}$ has coefficient:

Answer Key:

2

Step-by-Step Solution & Explanation

Using chain rule: $\frac{\partial w}{\partial x} = \frac{\partial w}{\partial u}(1) + \frac{\partial w}{\partial v}(1)$ and $\frac{\partial w}{\partial y} = \frac{\partial w}{\partial u}(-1) + \frac{\partial w}{\partial v}(1)$. Adding gives $\frac{\partial w}{\partial x} + \frac{\partial w}{\partial y} = 2 \frac{\partial w}{\partial v}$.
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