Question

Derivation `sqrt(a+2x)`?

Answer 1

`d/dx sqrt(a+2x) = 1/sqrt(a+2x)`

Explanation:

Assuming that `a` is a constant, then Using the chain rule, we can write:

`d/dx sqrt(a+2x) = d/dx (a+2x)^(1/2)`

`" " = 1/2(a+2x)^(1/2-1) d/dx(a+2x)`

`" " = 1/2(a+2x)^(-1/2) (2)`

`" " = 1/sqrt(a+2x)`

Answer 2

If `y=sqrt(a)+2x,then,(dy)/(dx)=0+2=2`.So,we take `y=sqrt(a+2x)`, then , `(dy)/(dx)=1/(sqrt(a+2x)`

Explanation:

`color(red)(d/(dx)(x^n)=n*x^(n-1))`
Now,
`y=sqrt(a+2x)=(a+2x)^(1/2)`
`:.(dy)/(dx)=1/2*(a+2x)^(1/2-1)d/(dx)(a+2x)` `=>(dy)/(dx)=1/cancel(2)*(a+2x)^color(red)(-1/2)*cancel(2)` `=>(dy)/(dx)=1/((a+2x)^(1/2))=1/(sqrt(a+2x)`