Question

How do you differentiate `y=4x^0.5-8lnx`?

Answer 1

`d/dx[4x^0.5 -8lnx] = (2sqrt(x)-8)/(x)`

Explanation:

`d/dx[4x^0.5 -8lnx]`
`= 2x^-0.5-8/x` ; power rule and derivative of natural logarithm
`= 2/(sqrt(x))-8/x`
`= (2sqrt(x))/(x)-8/x` ; rationalize the denominator
`= (2sqrt(x)-8)/(x)` ; simplify