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

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

Question:

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

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We have the following given data

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

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Applying the Rules of Differentiation to Calculate Derivatives

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Chapter 8 / Lesson 13
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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.


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