How do you find the derivative of sqrt(1-2x)12x?

2 Answers
Apr 28, 2016

dy/dx=(2x)/(2sqrt(1-2x)dydx=2x212x

Explanation:

Given -

y=sqrt(1-2x)y=12x

dy/dx=(2x)/(2sqrt(1-2x)dydx=2x212x

Apr 28, 2016

(-1)/sqrt(1-2x)112x

Explanation:

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