Question
Find the derivative of y = 3x (3 - x²)
Answers
GPT 3.5
To find the derivative of y = 3x(3 - x^2), we will use the product rule.
Let u = 3x and v = (3 - x^2).
Then, y = u*v.
To find dy/dx, we apply the product rule:
dy/dx = u * dv/dx + v * du/dx
dy/dx = 3x * (-2x) + (3 - x^2) * 3
dy/dx = -6x^2 + 9 - 3x^2
dy/dx = -9x^2 + 9
Therefore, the derivative of y = 3x(3 - x^2) is dy/dx = -9x^2 + 9.
Let u = 3x and v = (3 - x^2).
Then, y = u*v.
To find dy/dx, we apply the product rule:
dy/dx = u * dv/dx + v * du/dx
dy/dx = 3x * (-2x) + (3 - x^2) * 3
dy/dx = -6x^2 + 9 - 3x^2
dy/dx = -9x^2 + 9
Therefore, the derivative of y = 3x(3 - x^2) is dy/dx = -9x^2 + 9.