If y = 𝐼𝑛 √1+X − √1−X√1+X + √1−X , find dydX .

To find the derivative of the given function, we'll use the chain rule and the quotient rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. The quotient rule states that the derivative of a quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the square of the denominator.

Here's the step-by-step solution:

1. Rewrite the function to make it easier to differentiate: y = ln((√(1+X) - √(1-X)) / (√(1+X) + √(1-X)))

2. Differentiate using the chain rule and the quotient rule:

dy/dX = 1/((√(1+X) - √(1-X

To find the derivative of the given function, we'll use the chain rule and the quotient rule. Here are the steps:

1. Rewrite the function for clarity: y = ln((√(