Slope of Tangent Line for f(x)=x^3+x at (2,10) | Algebraic Method

[Mejiera]

Homework Statement

find the slope of the tangent line of f at the given point.

Homework Equations

f(x)= x^3 + x at (2,10)

The Attempt at a Solution

I know how to get the answer using the power rule, but I want to know the algebraic way of doing it
I get stuck at x^3 + x - 10/ x -2 how do I get rid of the x-2 in the bottom ?

 

[Bear_B]

f'(x) is the instantaneous rate of change at any x on the graph of f(x). In other words, f'(x) is the exact slope at any point on the graph of f(x). First, take the derivative of f(x). Then from there you can evaluate for any x (in your case x=2) to find the slope of your tangent line.