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

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Answer 1 · 2018-01-23T07:07:01

#f'(x) = 1/sqrt(1+2x) #

We must use the chain rule:

#d/(dx)( f (g(x) ) ) = f'( g(x) ) * g'(x) #

#=> sqrt(1+2x) = (1+2x)^(1/2) #

Hence Differentiasting the 'outside' function, leaving the inside function as it is, then multiplying by the direvative of the 'inside' function...

#f'(x) = 1/2 * (1+2x)^(-1/2) * d/(dx)(1+2x) #

#f'(x) = 1/2 ( 1+2x)^(-1/2) * 2#

#=> f'(x) = (1+2x)^(-1/2) = 1/sqrt(1+2x) #