Find {eq}f'(x) {/eq}.

{eq}f\left( x \right) = {{{x^2} + 2} \over {3x - 8}} {/eq}


Find {eq}f'(x) {/eq}.

{eq}f\left( x \right) = {{{x^2} + 2} \over {3x - 8}} {/eq}

Applying the Rules of Differentiation:

  • We differentiate a function to find another function that represents the rate of change of the function. If we have a function in the fraction form, we should apply the quotient rule of differentiation to obtain the derivative function.
  • The following formulas and rule of differentiation will be applied:

{eq}\begin{align} \hspace{1cm}\frac{dc}{dx} &=0 & \left[\text{ Where c is constant value } \right]\\[0.3cm] \hspace{1cm}\displaystyle \frac{d}{dx}x^n &=nx^{n-1} & \left[\text{ This is power rule of differentiation } \right]\\[0.3cm] \hspace{1cm}\displaystyle \frac{d}{dx}\left[ \dfrac{u}{v}\right]&=\dfrac{v \dfrac{du}{dx}-u\dfrac{dv}{dx}} {v^2}& \left[\text{ This is quotient rule } \right]\\[0.3cm] \end{align} {/eq}

Answer and Explanation: 1

Become a member to unlock this answer!

View this answer

We have the following given data

{eq}\begin{align} f\left( x \right) &=\frac{x^2 + 2}{3x - 8}\\[0.3cm] f'(x) & = \, ??...

See full answer below.

Learn more about this topic:

Applying the Rules of Differentiation to Calculate Derivatives


Chapter 8 / Lesson 13

The rules of differentiation are useful to find solutions to standard differential equations. Identify the application of product rule, quotient rule, and chain rule to solving these equations through examples.

Related to this Question

Explore our homework questions and answers library