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Parametric Differentiation

If y is a d...

Question

If $y$ is a differentiable function of $u$ and $u$ is a differentiable function of $x$ , then prove that $\frac{d y}{d x} = \frac{d y}{d u} . \frac{d u}{d x} .$

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Solution

Let $y = g (u)$
$u = h (x)$
$∴ \frac{d y}{d x} = \frac{d [g (u)]}{d x} = \frac{d [g (u)]}{d u} . \frac{d u}{d x}$
$= \frac{d y}{d u} . \frac{d u}{d x}$

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