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