How do you find the derivative of 1/x^8?

2 Answers
Nov 2, 2016

(dy)/(dx)=-8/x^9

Explanation:

Recall that 1/x^n=x^-n

:.1/x^8=x^-8

(dy)/(dx)=-8x^-9->power rule

=-8/x^9

OR

Using quotient rule, if y=1/x^8, let u=1 and v=x^8

(dy)/(dx)=(v(du)/(dx)-u(dv)/(dx))/v^2

(du)/(dx)=0

(dv)/(dx)=8x^7

:. (dy)/(dx)=(x^8*0-8x^7)/x^16

=(-8x^7)/x^16

=-8/x^9

=-8x^-9

Nov 2, 2016

d/dx(x^8) = -8/x^9

Explanation:

y = 1/x^8
implies y= x^-8
implies dy/dx= -8 x^(-8-1)
implies dy/dx= -8 x^-9
implies dy/dx = -8/x^9