Using Simpson role to find the denvatives of x=(y²+3x+7) (x²-4)
To find the derivative of the function x = (y^2 + 3x + 7)(x^2 - 4), we need to use the rules of differentiation. Since the function has both x and y variables, we need to use partial differentiation with respect to x.
Here are the steps to find the partial derivatives:
Step 1: Expand the given expression:
x = (y^2 + 3x + 7)(x^2 - 4)
= x^3y^2 + 3x^2y^2 + 7x^2 - 4y^2 - 12x - 28
Step 2: Take the partial derivative of this expression with respect to x. Treat y as a constant while differentiating with respect to x.
∂x/∂x = 3x^2y^2 + 6xy^2 + 14x - 12
So, the partial derivative of x with respect to x is 3x^2y^2 + 6xy^2 + 14x - 12.