Question

Differentiate.y = In [(x + 3)(x + 8)*(x + 4)]

Answer 1

Given function is

`y=\ln \lbrack(x+3)^5(x+8)^4(x+4)^6\rbrack`

Now, using the property of logarithm, y can be expressed as

`\begin{gathered} y=\ln (x+3)^5+\ln (x+8)^4+\ln (x+4)^6 \\ =3\ln (x+3)+4\ln (x+8)+6\ln (x+4) \end{gathered}`

Now, differentiating y w.r.t x,

`\begin{gathered} (d)/(dx)(y)=(3)/(x+3)+(4)/(x+8)+(6)/(x+4)_{} \\ =(13x^2+130x+288)/((x+3)(x+8)(x+4)) \end{gathered}`

So, the value of the derivative is

`(13x^2+130x+288)/((x+3)(x+8)(x+4))`