Question

How do you differentiate `f(x)=lnx * sin4x` using the product rule?

Answer 1

`(sin4x)/x + 4lnxcos4x`

Explanation:

`(lnx)'(sin4x) + (sin4x)'lnx`
`=(lnx) = 1/x`
`=(sin4x)' = (cos4x)(4x)' = 4cos4x`
`=1/x sin4x + 4cos4xlnx`
`=(sin4x)/x + 4 lnx cos4x`