Question

If y = x3 + 3x2 + 5, what is dy/dx

Answer 1

Please, use " ^ " to denote exponentiation: y = x^3 + 3x^2 + 5

Then the derivative of y with respect to x is dy/dx = 3x^2 + 6x (answer)

You could also write this result as dy/dx = 3x(x+6).

Answer 2

We need to find the derivative of that equation with respect to x. The derivative of x^3 is 3x^2, the derivative of 3x^2 is 6x, and the derivative of any constant is always 0. Use the power rule for derivatives that says
`(dy)/(dx)( x^(n))=n*x ^(n-1)`. Our derivative, then, is
`3x^2+6x`.