Question

найти производную под корнем х-1

Answer 1

1/2*корень из(х-1)........

Answer 2

Производная  (х-1) разделить(2*(корень (х-1) = 1 разделить на 2* корень (х-1) 

Answer 3

Finding the Derivative of √(x-1)

To find the derivative of √(x-1), we can use the chain rule. The chain rule states that if we have a composite function, such as f(g(x)), then the derivative of f(g(x)) with respect to x is given by f'(g(x)) * g'(x).

In this case, our function is f(x) = √x and g(x) = x-1. So, we can rewrite our original function as f(g(x)) = √(x-1).

To find the derivative, we need to find the derivatives of f(x) and g(x) and then apply the chain rule.

The derivative of f(x) = √x is given by f'(x) = 1 / (2√x).

The derivative of g(x) = x-1 is simply g'(x) = 1.

Now, we can apply the chain rule:

√(x-1)' = f'(g(x)) * g'(x) = (1 / (2√g(x))) * 1 = 1 / (2√(x-1))

Therefore, the derivative of √(x-1) is 1 / (2√(x-1)).

I hope this helps! Let me know if you have any further questions.