Question

differentiate y=root (x^2-1)

Answer 1

Step-by-step explanation:

dydx=x√x2−1

Explanation:

Let's equate the function to a variable y, so that

y=√x2−1

Now, I'll take another variable t and equate it as such,

t=x2−1

So that makes the y function as y=√t

Now, we are to find the derivative of y with respect to x. So that means we are to find dydx

Now, we can use chain rule to simplify our problem as

dydx=dydt⋅dtdx

That makes it, dydx=ddt(√t)⋅ddx(x2−1)

Now, we know that for any Real value n, ddx(xn)=nxn−1

, and that the derivative of a constant is zero. So

dydx=12√t⋅2x

Now, t was taken as t=x2−1, so substituting that back into the equation gives us the answer being searched for (after a few simplifications of course)