Final answer:
To find dy/dx for the function f(x) = (x+1)^2x, we can use the product rule for differentiation.
Step-by-step explanation:
To find dy/dx for the function f(x) = (x+1)^2x, we can use the product rule for differentiation. The product rule states that if we have two functions u(x) and v(x), then the derivative of their product is given by (u'v + uv').
In this case, let u(x) = (x+1)^2 and v(x) = x. Applying the product rule, we have:
f'(x) = u'(x)v(x) + u(x)v'(x)
Now, we need to find the derivatives of u(x) and v(x). Applying the chain rule, we have u'(x) = 2(x+1)(x+1)' = 2(x+1)(1) = 2(x+1).
And the derivative of v(x) is v'(x) = 1.
Substituting these values back into the product rule formula, we get:
f'(x) = 2(x+1)x + (x+1)^2(1)
Simplifying this expression gives f'(x) = 2x(x+1) + (x+1)^2.
Therefore, the correct answer is c) 2x(x+1)(2x-1).