# How do you find the derivative of #y=xln^3x#?

##### 1 Answer

#### Explanation:

We need to start with the product rule. Where

#dy/dx=(du)/dxv+u(dv)/dx#

Thus, where

#dy/dx=(d/dxx)ln^3x+x(d/dxln^3x)#

Now we have two internal derivatives we need to figure out. The first is basic:

For the second derivative, we need the chain rule. First, note that we have a function cubed:

Thus,

#dy/dx=1*ln^3x+x(3ln^2x)(d/dxlnx)#

Recall that

#dy/dx=ln^3x+3xln^2x(1/x)#

#dy/dx=ln^3x+3ln^2x#

If you wish:

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