Question

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

Answer 1

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

Explanation:

Product rule: `h = f*g`

`h'= fg'+gf'`

Note: `f(x) = ln x`

`f'(x) = 1/x`

Given `f(x) = (4-x^2)*lnx`

`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`