How to derive tan(2x) using the definition of the derivative ?

[faisal-tesla]

Homework Statement

Can someone please derive tan(2x) using the definition of the derivative?

Homework Equations

The Attempt at a Solution

I've tried to expand it but I couldn't get anywhere with it

thank you,

 

[LCKurtz]

Show us your first steps. Did you use the formula

$$\tan(a+b) = \frac{\tan a + \tan b}{1 - \tan a\tan b}$$

 

[faisal-tesla]

yes i did, but i used the identity tan 2x = 2tanx/ (1-tan^2(x) )

after that, it got messy when i plugged in (x+h)

 

[LCKurtz]

yes i did, but i used the identity tan 2x = 2tanx/ (1-tan^2(x) )

after that, it got messy when i plugged in (x+h)

Start with

$$\frac {\tan(2x + 2h)-\tan(2x)}{h}$$

and use the formula on the first term in the numerator.

 

[faisal-tesla]

I used both identities; it worked finally

thank you for your help . appreciated it.