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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