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The derivative of the function/ arctg(e^(3x)/(tsin2t))

You entered:

arctg(e^(3x)/(tsin2t))

What you mean?

atan(e^(3*x)/((tsin2*t)))
 
atan(e^(3*x)*t/tsin2)
 
atan(e^(3*x)*2*t/tsin)
 
atan(e^(3*x)*in2*t/ts)
 
atan(e*3*x/(tsin2*t))
 
atan(e*3*x*t/tsin2)
 
atan(e^(3*x)*in2*t/ts)

Derivative of arctg(e^(3x)/(tsin2t))

Function f() - derivative -N order at the point
v

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The solution

You have entered [src] 
    /   3*x \
    |  e    |
atan|-------|
    \tsin2*t/
atan⁡(e3xttsin2)\operatorname{atan}{\left(\frac{e^{3 x}}{t tsin_{2}} \right)} 
  /    /   3*x \\
d |    |  e    ||
--|atan|-------||
dx\    \tsin2*t//
∂∂xatan⁡(e3xttsin2)\frac{\partial}{\partial x} \operatorname{atan}{\left(\frac{e^{3 x}}{t tsin_{2}} \right)}
Transform
The first derivative [src] 
            3*x        
         3*e           
-----------------------
        /        6*x  \
        |       e     |
t*tsin2*|1 + ---------|
        |     2      2|
        \    t *tsin2 /
3e3xttsin2⋅(e6xt2tsin22+1)\frac{3 e^{3 x}}{t tsin_{2} \cdot \left(\frac{e^{6 x}}{t^{2} tsin_{2}^{2}} + 1\right)}
Simplify
The second derivative [src] 
  /                 6*x         \     
  |              2*e            |  3*x
9*|1 - -------------------------|*e   
  |              /        6*x  \|     
  |     2      2 |       e     ||     
  |    t *tsin2 *|1 + ---------||     
  |              |     2      2||     
  \              \    t *tsin2 //     
--------------------------------------
               /        6*x  \        
               |       e     |        
       t*tsin2*|1 + ---------|        
               |     2      2|        
               \    t *tsin2 /
9⋅(−2e6xt2tsin22⋅(e6xt2tsin22+1)+1)e3xttsin2⋅(e6xt2tsin22+1)\frac{9 \cdot \left(- \frac{2 e^{6 x}}{t^{2} tsin_{2}^{2} \cdot \left(\frac{e^{6 x}}{t^{2} tsin_{2}^{2}} + 1\right)} + 1\right) e^{3 x}}{t tsin_{2} \cdot \left(\frac{e^{6 x}}{t^{2} tsin_{2}^{2}} + 1\right)}
Simplify
The third derivative [src] 
   /                 6*x                        12*x          \     
   |              8*e                        8*e              |  3*x
27*|1 - ------------------------- + --------------------------|*e   
   |              /        6*x  \                            2|     
   |     2      2 |       e     |             /        6*x  \ |     
   |    t *tsin2 *|1 + ---------|    4      4 |       e     | |     
   |              |     2      2|   t *tsin2 *|1 + ---------| |     
   |              \    t *tsin2 /             |     2      2| |     
   \                                          \    t *tsin2 / /     
--------------------------------------------------------------------
                              /        6*x  \                       
                              |       e     |                       
                      t*tsin2*|1 + ---------|                       
                              |     2      2|                       
                              \    t *tsin2 /
27⋅(8e12xt4tsin24(e6xt2tsin22+1)2−8e6xt2tsin22⋅(e6xt2tsin22+1)+1)e3xttsin2⋅(e6xt2tsin22+1)\frac{27 \cdot \left(\frac{8 e^{12 x}}{t^{4} tsin_{2}^{4} \left(\frac{e^{6 x}}{t^{2} tsin_{2}^{2}} + 1\right)^{2}} - \frac{8 e^{6 x}}{t^{2} tsin_{2}^{2} \cdot \left(\frac{e^{6 x}}{t^{2} tsin_{2}^{2}} + 1\right)} + 1\right) e^{3 x}}{t tsin_{2} \cdot \left(\frac{e^{6 x}}{t^{2} tsin_{2}^{2}} + 1\right)}
Simplify
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