Question

What is the derivative of `sqrt(2x+1)`?

Answer 1

`1/sqrt(2x + 1)`

Explanation:

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

`d/dx [f(g(x) ] = f'(g(x)) . g'(x)`

rewrite `sqrt(2x + 1) " as " (2x + 1 )^(1/2)`

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

and g(x) = 2x + 1 → g'(x) = 2

hence : f'(g(x)) . g'(x) = `1/2(2x + 1)^(-1/2) . 2 = (2x + 1)^(-1/2)`

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