 Hello and welcome to the session. I am Deepika here. Let's discuss the question. If y is equal to determinant whose elements are fx, gx, hx, lm, n, a, b, c prove that dy by dx is equal to determinant f dash x, g dash x, h dash x, lm, n, a, b, c. So let's start the solution given y is equal to determinant gx, hx, lm, n, a, b, c. Therefore dy by dx is equal to, this is f dash x, g dash x, h dash x, lm, n, a, b, c. n, b, c, plus gx, hx, 0, 0, 0, because derivative of the constant is 0, a, b, c, plus hx, again this is 0, 0, 0, because derivative of the constant is 0. Therefore dy by dx is equal to, dash x, g dash x, h dash x, lm, n, a, b, c, plus 0, plus 0, by expansion of determinants we get this, because when we will expand we will get 0. This implies dy by dx is equal to determinant f dash x, g dash x, h dash x, lm, n, a, b, c, hence proved. I hope the question is clear to you, bye and have a nice day.