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

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  • $\large\frac{dy}{dx}=\frac{dy}{du}$$\times \large\frac{du}{dx}$
Step 1:
Let $u^9=y$
$u=3x^2-9x+5$
Differentiating with respect to $x$
$\large\frac{dy}{dx}=\frac{dy}{du}$$\times \large\frac{du}{dx}$
$y=u^{\large 9}$
$\large\frac{dy}{du}$$=9u^{9-1}\Rightarrow 9u^8$
$u=3x^2-9x+4$
Step 2:
Differentiating with respect to $x$
$\large\frac{du}{dx}$$=6x-9$
$\large\frac{dy}{dx}=\frac{dy}{du}$$\times \large\frac{du}{dx}$
$\quad\;=9u^8\times 6x-9$
$\quad\;=9[3x^2-9x+5]^8\times 6x-9$
$\quad\;=9[3x^2-9x+5]^8\times3[ 2x-3]$
$\quad\;=27[3x^2-9x+5]^8[ 2x-3]$
answered May 14, 2013 by sreemathi.v
edited May 14, 2013 by sreemathi.v
 

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