Derivative Question?

Question

How is the derivative of 
x^-7 ln x = 1-7lnx/x^8? 

Answer 1

The Function is x^ -7 ln(x)

By the formula d/ dx(uv) = uv' + v u'

u = x^ -7 and v = ln (x)

Now the derivative becomes

(x^ -7) (1/x) + ln (x)[-7 x^ (-7-1) ]    

(1 / x^7) (1 / x) + ln (x) [-7 (x^ -8) ]     [Since d/dx(x^n) = n x^(n -1) ] 

(1 / x^8) + ln (x) [-7 / x^8 ]

(1 - 7ln (x)) / (x^ 8) .

Henc ethe value of the function is  (1 - 7ln (x)) / (x^ 8) .