Differentiate the function ( 3 x^2 - 9x + 5 )^9 w.r.t to x. - Vidyadip

Question

Differentiate the function ${\left( {3{x^2} - 9x + 5} \right)^9}$ w.r.t to x.

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Answer

Let $y = {\left( {3{x^2} - 9x + 5} \right)^9}$

$\therefore \frac{{dy}}{{dx}} = 9{\left( {3{x^2} - 9x + 5} \right)^8}\frac{d}{{dx}}\left( {3{x^2} - 9x + 5} \right)$

$\left[ {\because \frac{d}{{dx}}{{\left\{ {f\left( x \right)} \right\}}^4} = n{{\left\{ {f\left( x \right)} \right\}}^{n - 1}}\frac{d}{{dx}}f\left( x \right)} \right]$

$\Rightarrow \frac{{dy}}{{dx}} = 9{\left( {3{x^2} - 9x + 5} \right)^8}\left[ {3\left( {2x} \right) - 9\left( 1 \right) + 0} \right] = 9{\left( {3{x^2} - 9x + 5} \right)^8}\left[ {6x - 9} \right]$

$ \Rightarrow \frac{{dy}}{{dx}} = 27{\left( {3{x^2} - 9x + 5} \right)^8}\left[ {2x - 3} \right]$

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