If y = left|begin{array}{ccc}f(x) & g(x) & h( | vedclass

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(A) Given that,$y = \left|\begin{array}{ccc}f(x) & g(x) & h(x) \ l & m & n \ a & b & c\end{array}ight|$.The derivative of a determinant is the sum

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$\left|\begin{array}{ccc}f^{\prime}(x) & g^{\prime}(x) & h^{\prime}(x) \ l & m & n \ a & b & c\end{array}ight|$

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(A) Given that,$y = \left|\begin{array}{ccc}f(x) & g(x) & h(x) \ l & m & n \ a & b & c\end{array}ight|$.The derivative of a determinant is the sum of determinants obtained by differentiating one row at a time while keeping other rows constant.$\frac{dy}{dx} = \left|\begin{array}{ccc}f^{\prime}(x) & g^{\prime}(x) & h^{\prime}(x) \ l & m & n \ a & b & c\end{array}ight| + \left|\begin{array}{ccc}f(x) & g(x) & h(x) \ 0 & 0 & 0 \ a & b & c\end{array}ight| + \left|\begin{array}{ccc}f(x) & g(x) & h(x) \ l & m & n \ 0 & 0 & 0\end{array}ight|$.Since a determinant with a row of zeros is equal to $0$,the second and third determinants vanish.Therefore,$\frac{dy}{dx} = \left|\begin{array}{ccc}f^{\prime}(x) & g^{\prime}(x) & h^{\prime}(x) \ l & m & n \ a & b & c\end{array}ight|$.

If $y = \left|\begin{array}{ccc}f(x) & g(x) & h(x) \\ l & m & n \\ a & b & c\end{array}\right|$,then $\frac{dy}{dx}$ is equal to

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