Differentiating tan2x: Steps & Solutions

[Trix1]

How do you differenciate tan2x and what are the steps?

 

[MarkFL]

Hello and welcome to MHB, Trix! :D

There are two rules you want to use here:

i) \(\displaystyle \frac{d}{dx}\left(\tan(x)\right)=\sec^2(x)\)

ii) \(\displaystyle \frac{d}{dx}\left(f(u(x))\right)=\d{f}{u}\d{u}{x}\)

Can you apply these rules, and get the correct derivative?

 

[Prove It]

How do you differenciate tan2x and what are the steps?

I'm going to assume that the OP doesn't already know the derivative of $\displaystyle \begin{align*} \tan{(x)} \end{align*}$, so you would need to write it as $\displaystyle \begin{align*} \frac{\sin{(2x)}}{\cos{(2x)}} \end{align*}$ and apply the Quotient Rule.