Question

How do you differentiate `f(x)=csc4x * tan2x` using the product rule?

Answer 1

`-4cot(4x)csc(4x)tan(2x)+2sec^2(x)csc(4x)`

Explanation:

The product rule states that,

`d/dx(uv)=u'v+uv'`

Here, `u=csc(4x)`, `v=tan(2x)`

`u'=-4cot(4x)csc(4x)`, `v'=2sec^2(x)`

Combining,

`d/dx(csc(4x)tan(2x))=-4cot(4x)csc(4x)tan(2x)+2sec^2(x)csc(4x)`