I need to find the second derivative of y=x(x-1)^1/2. I found the first derivative is 2x-1/2(x-1)^1/2, if someone could check, but I am miserably stuck on the second derivative.

In google type calc101

When you see list of results click on:
Calc101 com Automatic Calculus,linear Algebra,and Polynomals

When page be open click option derivatives

When that page be open in rectangle type your function and click option DO IT

Type your equtations like that:

x(x-1)^0.5

2x-1/2(x-1)^0.5

You will see first and second derivation step-by-step.

Thank you so much this definitely helps me double check my work!!

To find the second derivative of the function y = x(x-1)^(1/2), you'll need to apply the chain rule twice.

Let's start by finding the first derivative, which you correctly calculated as 2x - (1/2)(x-1)^(1/2).

Now, to find the second derivative, we need to differentiate the first derivative:

dy/dx = 2x - (1/2)(x-1)^(1/2)

To find the second derivative, we differentiate this expression once more using the product rule as follows:

d^2y/dx^2 = d/dx[2x] - d/dx[(1/2)(x-1)^(1/2)]

The derivative of 2x with respect to x is simply 2.

To differentiate the second term, you'll again need to apply the chain rule. The derivative of (x-1)^(1/2) with respect to x can be calculated by multiplying the exponent (1/2) by the derivative of the expression within the parentheses, which is 1. So we have:

d/dx[(1/2)(x-1)^(1/2)] = (1/2)*(1)*(x-1)^(-1/2)

Now, you can simplify and combine these terms to find the second derivative:

d^2y/dx^2 = 2 - (1/2)(x-1)^(-1/2)

And that's your final answer for the second derivative of y = x(x-1)^(1/2).