Question

How do you find the derivative of `y=sqrt(1+2x)`?

Answer 1

You can do this using the chain rule.

Explanation:

Let your function be `f(x)= sqrt(1 + 2x)`

Write as a composition of two functions:

`y = u^(1/2)`

`u = 1 + 2x`

The chain rule states that `dy/dx = dy/(du) xx (du)/dx`, or in language, "the derivative of function `u`. times the derivative of function `y`.

By the power rule we have that:

`y' = 1/2u^(-1/2)`

`y' = 1/(2u^(1/2))`

`u' = 2`

Now, multiplying both, we have:

`f'(x) = 2 xx 1/(2u^(1/2))`

`f'(x) = cancel(2)/(cancel(2)(u^(1/2))`

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

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

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

Hopefully this helps!