# Question #4ab09

##### 1 Answer

#### Explanation:

The slope of a function's tangent line at a point is given by the function's derivative. So, we need to find the derivative of

Note that *function* to the *also* multiply by the derivative of the inner function.

Thus,

So, the derivative of

#d/dx(x-5)^(1/2)=1/2(x-5)^(-1/2)*d/dx(x-5)#

The derivative of

#dy/dx=1/2(x-5)^(-1/2)=1/(2sqrt(x-5))#

The slope of the tangent line to the original function

#1/(2sqrt(9-5))=color(red)(1/4#