Question

How do you use the product rule to differentiate `sqrt(1+3x^2 )lnx^2`?

Answer 1

Solution

Explanation:

Let us assume the following

`u = sqrt(1+3x^2)`
`v = ln x^2`
`d(uv)= u .dv+v.du`
`d(uv) = sqrt(1+3x^2)\times1/x^2\times 2x + ln x^2 \times 1/(2sqrt(1+3x^2))\times6x`
`= (2sqrt(1+3x^2))/x+(3xlnx^2)/sqrt(1+3x^2)`

On further reduction will lead to
`(d(uv))/dx = (2+6x^2+3x^2ln x^2)/(xsqrt(1+3x^2))`