Question

How do you differentiate `f(x)=ln2x * sin3x` using the product rule?

Answer 1

`f(x)=ln2x * sin3x`

Applying product rule,
When, `f(x)=g(x)*h(x)`
`f'(x)=g'(x)h(x)+g(x)h'(x)`

`=>f'(x)=(ln2x)' sin3x+ln2x (sin3x)'`

`=>f'(x)=[1/(2x)xx2xxsin3x]+[ln2x xxcos3x xx3]`

`=>f'(x)=1/xsin3x+3ln2xcos3x`