Calculating the Derivative

[smgrojean]

How do I calculate the first derivative of (sin(x))/(cos(2x)) ?

I got to this point but then I got stuck (I am assuming that I got to the right point).

 

[pka]

How do I calculate the first derivative of (sin(x))/(cos(2x)) ?

I got to this point but then I got stuck (I am assuming that I got to the right point).View attachment 2331

It should be
\(\displaystyle \dfrac{\cos(x)\cdot\cos(2x)+2\sin(x)\cdot\sin(2x)}{(\cos^2(2x))}\)

 

[HallsofIvy]

What is the derivative, with respect to x, of cos(2x)?

 

[math1]

derivative

-sin(2x).(2)

 

[lookagain]

-sin(2x).(2)

Please do not use a dot/period to show multiplication.


For examples, these are suggestions.



(-sin(2x))(2) or

[-sin(2x)](2) or

-2sin(2x)

 

[smgrojean]

It should be
\(\displaystyle \dfrac{\cos(x)\cdot\cos(2x)+2\sin(x)\cdot\sin(2x)}{(\cos^2(2x))}\)

I might be wrong but I do not see a way to simplify that anymore, am I correct?

 

[Deleted member 4993]

Simplicity is in the eye of the beholder (grader).

To me - this is simple enough!!!

 

[HallsofIvy]

...beerholder?

Certainly, I always found it easier to grade homework while holding a beer!