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C3 query really bugging me watch

1. The curve has the equation, 'y= e^2x tanx'.
I am asked to show the turning points on this curve occur where
'tanx = 1'

I differentiated the equation and got:
2e^2x . tanx + e^2x sec^2 x = 0

then I took 'e^2x' out so that I have:

e^2x (2tanx + sec^2 x) = 0

afterwards, I changed 'sec^2 x' into '1+tan^2 x' so....

e^2x (2tanx + 1+tan^2 x) = 0

I sense that I need to factorise it, but how do the get rid of the
'e^2x' outside the brackets
2. (Original post by W.H.T)
The curve has the equation, 'y= e^2x tanx'.
I am asked to show the turning points on this curve occur where
'tanx = 1'
this means that when you equate dy/dx to 0, you need to simplify it until you get tanx - 1 = 0

so you can just divide by the e^2x
3. e^2x=0

or
2 tanx+1+tan^2x=0

I think. Then factorise the tans.
4. (Original post by W.H.T)

e^2x (2tanx + 1+tan^2 x) = 0

I sense that I need to factorise it, but how do the get rid of the
'e^2x' outside the brackets
divide 0 by e^2x. Simples
5. (Original post by TylerDurden)
e^2x=0

or
2 tanx+1+tan^2x=0

I think. Then factorise the tans.
noting of course that e^2x cannot equal 0
6. Divide both sides by e2x
(tanx+1)2=0
7. can not equal 0.
Therefore, simply factorise
and you would therefore get:

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