Find the Derivative

[mhunt1739]

Find the Derivative-

y= [(- sqrt(x^2+4))/(2x^2)] - 1/4ln[(2+sqrt(x^2+4))/x]

I know how to find the derivative of the first part of the function but i am not sure how to find the derivative of an ln funtion that is a fraction- or with the -1/4 in front of it. Thanks!

 

[dts5044]

the fraction -1/4 is a constant, so you can take the derivative of ln[(2+sqrt(x^2+4))/x] and multiply by -1/4 at the end

to illustrate, the derivative of y = 3x^(2) is

y' = 3 *2x^(1)

(see how the constant stays and multiplies the derivative of the x term)

the derivative of lnu is: u'/ u

so take the derivative of what is inside the ln function, that is your u',

just divide that value by what is inside the ln function to take the derivative of that section of the equation!

i.e. the derivative of -1/4 lnu is:

-1/4 * u'/u