Question

How do you use the chain rule to differentiate `y=sqrt(3x^2+4x)`?

Answer 1

I found: `(dy)/(dx)=(6x+4)/(2sqrt(3x^2+4x))`

Explanation:

We first differentiate the square root leaving the argument as it is and multiply by the differential of the argument (red):
We can write:
`y=sqrt(3x^2+4x)=(3x^2+4x)^(1/2)`
so we get:
`(dy)/(dx)=1/2(3x^2+4x)^(1/2-1)color(red)((6x+4))=1/2(3x^2+4x)^(-1/2)color(red)((6x+4))=`
so we get:
`(dy)/(dx)=(6x+4)/(2sqrt(3x^2+4x))`