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

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Answer 1 · 2016-06-25T15:44:46

You can do this using the chain rule.

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!