# How do you find the slope of the curve #f(x)=sqrt(x-1)# at the point x=5?

##### 1 Answer

The slope is

(there are two possible values as the function is not one-one as it contains a square root)

#### Explanation:

The slope of a function at some particular value of the independent variable is the first derivative evaluated at that particular value.

Denoting the two component functions as

and

it might be noted that

The chain rule states

#= g'(h(x))h'(x) #

That is, the derivative of the outer function evaluated at the inner function times the derivative of the inner function.

It is convenient to write

so that the rules of polynomial differentiation might be easily applied

evaluating this at the value of the inner function

Noting

The overall derivative is

That is

so