# How do you differentiate #f(x)= (4-x^2) *ln x# using the product rule?

##### 1 Answer

Jan 2, 2016

#### Explanation:

Product rule:

#h'= fg'+gf'#

Note:

#f'(x) = 1/x#

Given

#f'(x) = (4-x^2) d/dx(lnx) + lnx *d/dx(4-x^2)#

#= (4-x^2) (1/x) + -2x(lnx)#

# = (4-x^2)/x - (2x) (ln x) # =

#((4-x^2)-2x^2 * lnx)/x#