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

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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?
 
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Correct, good work
 
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.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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