Question

If y=√x\lnx, then y′(e^2)=?
use quotient rule

Answer 1

HI :DDD

Answer 2

\[\large y=\frac{\sqrt{x}}{\ln(x)}\]?

Answer 3

yes

Answer 4

\[\left(\frac{f}{g}\right)'=\frac{gf'-fg'}{g^2}\] with
\[f(x)=\sqrt{x},f'(x)=\frac{1}{2\sqrt{x}},g(x)=\ln(x), g'(x)=\frac{1}{x}\] most of it will be annoying algebra

Answer 5

first step is just to plug that stuff in to the quotient rule, start with
\[\large\frac{\ln(x)\times\frac{1}{2\sqrt{x}}-\sqrt{x}\times \frac{1}{x}}{(\ln(x))^2}\]

Answer 6

got it, yea i was a bit confused on how to set it up. thanks!

Answer 7

next step is probably to get rid of obnoxious compound fraction by multiplying top and bottom by \(2x\)

Answer 8

yw