Evaluate the derivative of the function at the given point ,use graphing utility to verify it

Question

f(x) = 5/(x^3 - 2)   (-2,-1/2)

Answer 1

Step 1 :

The function is and the point .

Rewrite the expression :

Differentiate with respect to x.

Use chain rule : .

Derivative of the function :

Step 2 :

Substitute in above equation :

Derivative of the function at is

Step 3 :

Graph of the differential function .

 

Solution :

Derivative of the function at is