Question

What is the derivative of `(3+2x)^(1/2)`?

Answer 1

`1/((3+2x)^(1/2))`

Explanation:

`"differentiate using the "color(blue)"chain rule"`

`"given "y=f(g(x))" then"`

`dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"`

`rArrd/dx((3+2x)^(1/2))`

`=1/2(3+2x)^(-1/2)xxd/dx(3+2x)`

`=1(3+2x)^(-1/2)=1/((3+2x)^(1/2))`

Answer 2

`1/(sqrt(3+2x))`

Explanation:

If
`f(x)=(3+2x)^(1/2)=(sqrt(3+2x))`

(apply the chain rule)

`u=3+2x`

`u'=2`

`f(u)=u^(1/2)`

`f'(u)=(1/2) (u)^(-1/2) times u'`

Hence:

`f'(x)=(1/2) (3+2x)^(-1/2) times 2`

`f'(x)=(3+2x)^(-1/2)`

`f'(x)=(1)/(sqrt(3+2x))`