Derivative of (2+3sinx)(4+5cosx)tanx

[Sakha]

Homework Statement

Derive the following:
f(x)= (2+3sinx)(4+5cosx)tanx



2. The attempt at a solution
I derive it and got
f'(x)=(4+5)tanx(3cosx)+(2+3sinx)(tanx(-5sinx)+sec²x(4+5cosx))

Can someone confirm if this is right?

 

[Awatarn]

Correct, good work

 

[Sakha]

Thanks!
I put it first on WolframAlpha to compare, but it does the product rule the other way I did so I didnt felt like simplifying.