Differentiate the functions given w.r.t. x:
`(x+3)^2.(x+4)^3.(x+5)^4`

Explanation

Let `y=(x+3)^2*(x+4)^3*(x+5)^4`

Taking log on both sides

`logy=log((x+3)^2*(x+4)^3*(x+5)^4)`

`logy=log((x+3)^2+(x+4)^3+(x+5)^4)`

`logy=2log((x+3)+3(x+4)+4(x+5))`

Differ. both sides w.r.t.x
`(d(logy)/dx)=(d(2log((x+3)+3(x+4)+4(x+5))))/dx`


`(d(logy)/dx)(dy)/dx=(d(2log(x+3)))/dx+(d(3log(x+4)))/dx+(d(4log(x+5)))/dx`


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