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If y=|(f(x),g(x),h(x)),(l, m, n),( a, b,...

If `y=|(f(x),g(x),h(x)),(l, m, n),( a, b, c)|`, prove that `(dy)/(dx)=|(fprime(x),gprime(x),hprime(x)),(l, m, n),( a, b, c)|`

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To prove that if \( y = \begin{vmatrix} f(x) & g(x) & h(x) \\ l & m & n \\ a & b & c \end{vmatrix} \), then \( \frac{dy}{dx} = \begin{vmatrix} f'(x) & g'(x) & h'(x) \\ l & m & n \\ a & b & c \end{vmatrix} \), we will follow these steps: ### Step 1: Write the determinant We start with the determinant: \[ y = \begin{vmatrix} f(x) & g(x) & h(x) \\ l & m & n \\ a & b & c \end{vmatrix} \] ...
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