Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(i) `(3x^2+2)^2`
(ii) `(x+2)(x+3)`

Explanation

(i) Product rule :


Let `u=3 x^{2}+2 ; v=3 x^{2}+2`

Then,`u'=6 x ; v'=6 x`

Using the product rule :

`\frac{d}{d x}(u v)=u v'+v u'`

`\frac{d}{d x}[(3 x^{2}+2)(3 x^{2}+2)]=(3 x^{2}+2)(6 x)+(3 x^{2}+2)(6 x)`


Other method:


`=18 x^{3}+12 x+18 x^{3}+12 x `

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