Question

What is the derivative of:
x-1/x^(1/2)

Their answer is 1/2x^(1/2)+1/2x^(3/2)

Answer 1

Simplify before taking a derivative, so as to avoid the quotient rule :) Split it into 2 fractions.\[\huge \frac{x}{x^{1/2}}-\frac{1}{x^{1/2}}\]

Answer 2

Simplifying further gives us...
\[\huge x^{1/2}-x^{-1/2}\]If this step confuses you, let me know :D

Answer 3

Taking the derivative, applying the power rule to each term gives us...
\[\huge \frac{1}{2}x^{-1/2}-\left(-\frac{1}{2}x^{-3/2}\right)\]

Answer 4

Yes Thats it! Thanks
splitting into 2 fractions :/ forgot about that step