Question

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

Answer 1

`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)`