If `y =| [f(x) , g(x) , h(x)], [l , m , n], [a , b , c] |` , prove that `(dy)/(dx)=|f^(prime)(x)g^(prime)(x)h^(prime)(x)l m n a b c|` .

Explanation

To prove that \(\frac{dy}{dx} = |f'(x) \quad g'(x) \quad h'(x) \quad l \quad m \quad n \quad a \quad b \quad c|\), we will use the properties of determinants and the concept of differentiation.

### Step 1: Write the determinant
We start with the determinant given by:
\[
y = \begin{vmatrix}
f(x) & g(x) & h(x) \\
l & m & n \\
...