Rewrite the function by splitting the fraction and using trigonometric identities.

Let's find the derivative (dy)/(dx) for the given function. The function is y = ( x^2 - 3 p^2)/( x^2). We will assume "Sn" means and p is a constant with respect to x. Step 1: Rewrite the function by splitting the fraction and using trigonometric identities. y = ((x^2))/((x^2)) - (3(p^2))/((x^2)) y = (x^2) - 3(p^2) · (x^2) Step 2: Differentiate the first term, (x^2), using the chain rule. Let u = x^2. Then (du)/(dx) = 2x. The derivative of (u) is ^2(u) · (du)/(dx). (d)/(dx)((x^2)) = ^2(x^2) · 2x = 2x^2(x^2) Step 3: Differentiate the second term, -3(p^2) · (x^2). Since p is a constant, 3(p^2) is also a constant. Let C = 3(p^2). We need to find (d)/(dx)(-C (x^2)). The derivative of (u) is (u)(u) · (du)/(dx). Here, u = x^2, so (du)/(dx) = 2x. (d)/(dx)(-C (x^2)) = -C · ((x^2)(x^2) · 2x) Substitute C = 3(p^2) back: = -3(p^2) · 2x(x^2)(x^2) = -6x(p^2)(x^2)(x^2) Step 4: Combine the derivatives of both terms. (dy)/(dx) = 2x^2(x^2) - 6x(p^2)(x^2)(x^2) The final answer is (dy)/(dx) = 2x^2(x^2) - 6x(p^2)(x^2)(x^2). Last free one today — make it count tomorrow, or type /upgrade for unlimited.