Question

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

Answer 1

`f'(x)=e^(2x)[lnx(x^2-4)+2xlnx+1/x(x^2-4)]`

Explanation:

#To differentiate the product of 3 functions

`(abc)'=a'bc+b'ac+c'ab`

`rArra=e^(2x)rArra'=e^(2x).d/dx(2x)=2e^(2x)`

`b=x^2-4rArrb'=2x`

`"and " c=lnxrArrc'=1/x`

`rArrf'(x)=2e^(2x)(lnx(x^2-4))+2x(e^(2x)lnx)+1/x(e^(2x)(x^2-4))`

`=e^(2x)[lnx(x^2-4)+2xlnx+1/x(x^2-4)]`