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

1 Answer
Jim G.
Mar 30, 2016

#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) #

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