course mth 271
mr smith: i follow your work until you go from 1/sqroot x to 1/2sqrootx i dont understand where that is coming from. i still get confused on when to use the chain rule vs when y=lnx so y'=1/x would be appropriate.
Since x^(-1/2) = 1 / x^(1/2) = 1 / sqrt(x) we have y ' = 1 / (2 sqrt(x)).if you have y=sqrootx then y=1/2x^-.5 isnt that the deriv?
The statement 'Since x^(-1/2) = 1 / x^(1/2) = 1 / sqrt(x) we have y ' = 1 / (2 sqrt(x))' is incorrect; if it's my statement then it was a bad oversight on my part.
Here are two correct statements:
If y = sqrt(x), then since x^(1/2) = sqrt(x) we have y ' = (x^(1/2)) ' = 1/2 x^(1/2 - 1) = 1/2 x^(-1/2).
If y = 1 / sqrt(x), then since x^(1/2) = sqrt(x) we have y = 1 / (x^(1/2)) = x^(-1/2), and y ' = (x^(-1/2)) ' = -1/2 x^(-1/2 - 1) = -1/2 x^(-3/2).