Derivative simplification

Hi Rajesh, let's simplify this derivative expression step by step. We'll start with the initial form shown at the top of your image.

We start with dy over dx equals one over two times the square root of the fraction a squared plus x squared over a squared minus x squared, all multiplied by four x a squared over the quantity a squared minus x squared squared.

First, let's simplify the square root in the denominator by flipping the fraction inside the root and moving it to the numerator.

Next, we can simplify the factors of two and four. Four divided by two leaves us with two in the numerator.

Now, let's express the square root as fractional powers to help us combine terms.

Notice that we have a squared minus x squared in both parts. We can subtract the exponent in the numerator from the one in the denominator. That is, two minus one half, which is three halves.