- #1

Helly123

- 581

- 20

## Homework Statement

$$y = x.\log_e {\sqrt{x}}$$

## Homework Equations

f(x) = g(x) h(x)

f ' (x) = g ' (x) . h (x) - h ' (x) . g(x)

## The Attempt at a Solution

$$y = x .\log_e {\sqrt {x}}$$

$$y '(x) = 1.ln \sqrt{x} + \frac{1}{2} $$

the right answer is

$$ y ' = \log_{10} {\sqrt{x}} + \frac{1}{2} $$

$$ Is \ \log_e {\sqrt{x}} = \log_{10} {\sqrt{x}} \ ? $$

Second Try:

$$ y = x \log_e {\sqrt{x}} $$

$$ y = \log_e {x^{x/2}} $$

$$y ' = \frac{1}{x^{x/2}} . \frac{x}{2} . x^{(x-2)/2}$$

$$ y ' = \frac{1}{2}$$

why different result?