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(Solved): 4. Let f:RnRn be a differentiable map given by f(x1,,xn)=(y1, ...

$4. Let \( f: \mathbb{R}^{n} \rightarrow \mathbb{R}^{n} \) be a differentiable map given by \( f\left(x_{1}, \ldots, x_{n}\rig$ ???????

4. Let

f : R^{n} ? R^{n}

be a differentiable map given by

f (x_{1}, \dots, x_{n}) = (y_{1}, \dots, y_{n})

and let

? = d y_{1} ? ? ? d y_{n}

. Show that

f^{?} w = det (df) ? d x_{1} ? ? ? d x_{n}

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