### Home > CALC > Chapter Ch3 > Lesson 3.4.2 > Problem 3-169

3-169.

Use the *definition of a derivative* as a limit to find *f *′(*x*) if *f*(*x*) = 2*x* + 9. Use the Power Rule to confirm your solution. Homework Help ✎

Hana's definition of the derivative:

Substitute *f*(*x*) into Hana's definition of the derivative.

Expand the numerator and combine like terms.

Factor out an *h* from the numerator so you can 'cancel out' the *h* from the denominator.

Evaluate the limit as *h* →0. This will give you *f* '(*x*).

Confirm that the *f* '(*x*) you found Algebraically agrees with what you get using the Power Rule.