How to find the derivative of sqr lnx

Question

campbell_st · Answer

use the function of a function rule 

$$y = (\ln(x))^\frac{1}{2}$$

let u = ln(x)

campbell_st · Answer

so you have 

$$y = u^{\frac{1}{2}}$$

so find dy/du

amd also find du/dx

then you can use 

$$\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dy}$$

which is called function of a function or the chain rule...

anonymous · Answer

i was taught the rule of taking the derivative of ln, 

its 1/f(x) multiplied by the derivative of that function, multiplied by the lnf(x) . but when I do it, i et the wrong answer

campbell_st · Answer

oopps should read 

$$\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$$

campbell_st · Answer

well start with dy/du

$$\frac{dy}{du} = \frac{1}{2\sqrt{u}}$$

and 

$$\frac{du}{dx} =\frac{1}{x}$$

campbell_st · Answer

so now substitute u = ln(x) into dy/du

$$\frac{dy}{dx} = \frac{1}{2\sqrt{\ln(x)} }\times \frac{1}{x}$$

just simplify

anonymous · Answer

could you help with another question

campbell_st · Answer

just post it... as a new question and someone will help