Example of Chain Rule for differentiation. Find $y'$ if $y=\left( \left( 3x^2+2\right)^4+1\right)^5$.

Example of Chain Rule for differentiation. 
Find $y'$ if $$y=\left( \left( 3x^2+2\right)^4+1\right)^5$$
The chain rule for differentiation is really quite simple. You just differentiate the 'outside function' first. Then multiply by the derivative of the 'inside function'. Easy peasy :-)

$\displaystyle y'=5\left( \left( 3x^2+2\right)^4+1\right)^4\times 4\left( 3x^2+2\right)^3\times 6x$

$\displaystyle y'=120x\left( 3x^2+2\right)^3\left( \left( 3x^2+2\right)^4+1\right)^4$