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

1 Answer
AJ Speller
Sep 11, 2014

Convert the square root to its exponential form and then use the power rule.

#y=sqrt(x)=x^(1/2)#

Now bring the power of #1/2# down as a coefficient and then subtract 1 from the current power of #1/2#. Evaluate the fractions and simplify. Manipulate exponents from negative to positive.

#y'=1/2x^((1/2-1))=1/2x^((1/2-2/2))=1/2x^((-1/2))=1/(2x^(1/2))=1/(2sqrt(x))#

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