### Home > CALC > Chapter 3 > Lesson 3.4.2 > Problem3-169

3-169.

Use the definition of a derivative as a limit to find $f^\prime(x)$ if $f(x) = 2x + 9$. Use the Power Rule to confirm your solution.

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 $f^\prime(x)$.

Confirm that the $f^\prime(x)$ you found Algebraically agrees with what you get using the Power Rule.