Differentiating tan2x: Steps & Solutions

The derivative would be $\displaystyle \begin{align*} \frac{2\cos^2{(2x)}+2\sin^2{(2x)}}{\cos^2{(2x)}} \end{align*}$. In summary, to differentiate $\displaystyle \tan{(2x)}$, you would need to use the Quotient Rule and the derivatives of $\displaystyle \tan{(x)}$ and $\displaystyle \sin{(x)}$.
  • #1
Trix1
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0
How do you differenciate tan2x and what are the steps?
 
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  • #2
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?
 
  • #3
Trix said:
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.
 

FAQ: Differentiating tan2x: Steps & Solutions

1. What is the definition of tan2x?

Tan2x is a mathematical function that calculates the tangent of twice the angle x.

2. What are the steps for differentiating tan2x?

The steps for differentiating tan2x are as follows:
1. Rewrite tan2x as sin2x/cos2x
2. Use the quotient rule to differentiate sin2x/cos2x
3. Simplify the resulting expression
4. Replace sin2x and cos2x with their respective trigonometric identities
5. Simplify the final expression to get the derivative of tan2x.

3. What is the derivative of tan2x?

The derivative of tan2x is 2sec2x.

4. What is the solution to differentiating tan2x?

The solution to differentiating tan2x is 2sec2x.

5. Are there any special cases when differentiating tan2x?

Yes, there is a special case when differentiating tan2x. If the angle x is equal to π/4 or 45 degrees, the derivative of tan2x is undefined as the function is discontinuous at this point.

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