d/dx of (sqrt of (x-1))?

Answer 1

The basic formula for differentiation of x^n is n.x^(n-1).
So your problem can be re-written as (x-1)^1/2.

Here n is 1/2

Therefore n.x^(n-1) gives (1/2).(x-1)^(1/2-1) (multiplied by 1)

Now (1/2-1) is -(1/2).Therefore the entire expression becomes (1/2).(x-1)^(-1/2)

Now this can be written as 1/{(2(x-1)^1/2)}

That is we are bringing that -1/2 down and it becomes positive.

But anything to the power of 1/2 is the root of that 'anything'.

So your final answer should be

1
------------------
2(sqrt of (x-1))

Remember the differention of the bracket term,that is (x-1) is 1. As d/dx(x) is one and -1 is a constant. Hence that multiplied by one in the third sentence.

Answer 2

1/(2*sqrt(x-1))

Answer 3

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