What is the second derivative of 1/x^2?

2 Answers
Jan 21, 2016

f''(x) = 6/x^4

Explanation:

rewrite f(x) = 1/x^2 = x^-2

rArr f'(x) = -2x^-3

rArr f''(x) = 6x^-4 = 6/x^4

Jan 21, 2016

y''=6x^-4=6/x^4

Explanation:

y=1/x^2

y''=d/(dx)y'=(d^2y)/dx^2

To find y' e y'' you can use the Power Rule:

given:

y=x^n => y'=nx^(n-1)

Remembering the power proprerties: 1/a^n=a^(-n)

y=1/x^2=x^(-2)=>y'=-2x^(-2-1)=-2x^-3

y''=d/(dx)(-2x^-3)=-2d/(dx)x^-3=-2*(-3)x^(-3-1)=

=6x^-4=6/x^4