Question

How do you find the derivative of `sqrt(1-2x)`?

Answer 1

`dy/dx=(2x)/(2sqrt(1-2x)`

Explanation:

Given -

`y=sqrt(1-2x)`

`dy/dx=(2x)/(2sqrt(1-2x)`

Answer 2

`(-1)/sqrt(1-2x)`

Explanation:

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

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

rewrite `sqrt(1-2x) = (1-2x)^(1/2)`

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

and g(x) = 1-2x → g'(x) = -2

`rArr d/dx(sqrt(1-2x))=1/2(1-2x)^(-1/2).(-2)`

`= (-1)/(1-2x)^(1/2) = (-1)/(sqrt(1-2x))`