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Matrix derivatives

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Show that if f1(x), f2(x), g1(x) and g2(x) are differentiable functions, and if

W =
|f1(x) f2(x)|
|g1(x) g2(x)|

then dW/dx =
|f'1(x) f'2(x)|
|g1(x) g2(x) |

+

|f1(x) f2(x)|
|g'1(x) g'2(x)|

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Solution Summary

This shows how to determine the derivative of a matrix of differentiable functions.

Solution Preview

If f1 and f2 be two differentiable functions. The Wronskian W is given as
|f1 f2 |
|f1' ...

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