To find the derivative of the function y = (x^2 + 2x)(2x - 1), we can apply the product rule, which states that if we have a function that is the product of two functions, u and v, then the derivative of the product is given by:
d/dx(uv) = u * (dv/dx) + v * (du/dx)
Let's differentiate the given function step by step using the product rule:
u = x^2 + 2x
v = 2x - 1
Now, let's find the derivatives of u and v:
du/dx = d/dx(x^2 + 2x) = 2x + 2
dv/dx = d/dx(2x - 1) = 2
Now, we can apply the product rule:
d/dx[(x^2 + 2x)(2x - 1)] = (x^2 + 2x) * (2) + (2x - 1) * (2x + 2)
Simplifying further:
= 2x^2 + 4x + 4x^2 + 4x - 2
= 6x^2 + 8x - 2
Therefore, the derivative of y = (x^2 + 2x)(2x - 1) is 6x^2 + 8x - 2.