How do you find the derivative of (-2)/(x(ln x)^3). ?

1 Answer
Feb 20, 2018

dy/dx=2(ln(x)+3)/(x^2ln(x)^4)

Explanation:

We want to find the derivative of

y=-2/(xln(x)^3)=-2x^-1/ln(x)^3

Use the quotient rule if y=f/g then

dy/dx=(f'g-fg')/g^2

Here f=x^-1=>f'=-x^-2 and g=ln(x)^3=>g'=3ln(x)^2/x

dy/dx=-2(-x^-2ln(x)^3-x^-1 3ln(x)^2/x)/ln(x)^6

=-2(-x^-2ln(x)^3-3ln(x)^2x^-2)/ln(x)^6

=2(ln(x)^3+3ln(x)^2)/(x^2ln(x)^6)

=2(ln(x)+3)/(x^2ln(x)^4)