Question

whats the derivative of y=sqrt(x)/x?

Answer 1

step by step please

Answer 2

\[y=\frac{\sqrt x} x=\frac{x^{1/2}}{x^1}=x^{1/2-1}=x^{-1/2}\]

Answer 3

now take the derivative

Answer 4

\[y=x^n\]
\[y'=nx^{n-1}\]

Answer 5

how come after x^1/2 / x^1 it becomes x^x/2-1?

Answer 6

because
\[\frac {1}{a^m}=a^{-m}\]
\[\frac a{a^n}=a\times a^{-n}=a^{1-n}\]

Answer 7

understand ?