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18*e^x/tanh(x)
The derivative of the function/ 18*e^x/tanh(x)

You entered:

18*e^x/tanh(x)

What you mean?

18*e^x/tanh(x)
 
18*e^x*x/tanh(x)
 
18*e^x/tanh(x)
 
18*e^x*x/tanh(x)
 
18*e*x/tanh(x)
 
18*e*x*x/tanh(x)
 
18*e^x*x/tanh(x)

Derivative of 18*e^x/tanh(x)

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

The graph:

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Piecewise:

The solution

You have entered [src] 
     x 
 18*e  
-------
tanh(x)
18extanh⁡(x)\frac{18 e^{x}}{\tanh{\left(x \right)}} 
  /     x \
d | 18*e  |
--|-------|
dx\tanh(x)/
ddx18extanh⁡(x)\frac{d}{d x} \frac{18 e^{x}}{\tanh{\left(x \right)}}
Transform
The graph
02468-8-6-4-2-1010-500000500000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     x       /         2   \  x
 18*e     18*\-1 + tanh (x)/*e 
------- + ---------------------
tanh(x)              2         
                 tanh (x)
18(tanh⁡2(x)−1)extanh⁡2(x)+18extanh⁡(x)\frac{18 \left(\tanh^{2}{\left(x \right)} - 1\right) e^{x}}{\tanh^{2}{\left(x \right)}} + \frac{18 e^{x}}{\tanh{\left(x \right)}}
Simplify
The second derivative [src] 
   /      /         2   \                     /              2   \\   
   |    2*\-1 + tanh (x)/     /         2   \ |     -1 + tanh (x)||  x
18*|1 + ----------------- + 2*\-1 + tanh (x)/*|-1 + -------------||*e 
   |         tanh(x)                          |            2     ||   
   \                                          \        tanh (x)  //   
----------------------------------------------------------------------
                               tanh(x)
18⋅(2(tanh⁡2(x)−1tanh⁡2(x)−1)(tanh⁡2(x)−1)+2(tanh⁡2(x)−1)tanh⁡(x)+1)extanh⁡(x)\frac{18 \cdot \left(2 \left(\frac{\tanh^{2}{\left(x \right)} - 1}{\tanh^{2}{\left(x \right)}} - 1\right) \left(\tanh^{2}{\left(x \right)} - 1\right) + \frac{2 \left(\tanh^{2}{\left(x \right)} - 1\right)}{\tanh{\left(x \right)}} + 1\right) e^{x}}{\tanh{\left(x \right)}}
Simplify
The third derivative [src] 
   /                                                                                                             /              2   \\   
   |                                                                                             /         2   \ |     -1 + tanh (x)||   
   |                                              2                                        3   6*\-1 + tanh (x)/*|-1 + -------------||   
   |                               /         2   \      /         2   \     /         2   \                      |            2     ||   
   |        1            2      10*\-1 + tanh (x)/    3*\-1 + tanh (x)/   6*\-1 + tanh (x)/                      \        tanh (x)  /|  x
18*|-4 + ------- + 4*tanh (x) - ------------------- + ----------------- + ------------------ + --------------------------------------|*e 
   |     tanh(x)                          2                    2                   4                          tanh(x)                |   
   \                                  tanh (x)             tanh (x)            tanh (x)                                              /
18⋅(6(tanh⁡2(x)−1tanh⁡2(x)−1)(tanh⁡2(x)−1)tanh⁡(x)+6(tanh⁡2(x)−1)3tanh⁡4(x)−10(tanh⁡2(x)−1)2tanh⁡2(x)+3(tanh⁡2(x)−1)tanh⁡2(x)+4tanh⁡2(x)−4+1tanh⁡(x))ex18 \cdot \left(\frac{6 \left(\frac{\tanh^{2}{\left(x \right)} - 1}{\tanh^{2}{\left(x \right)}} - 1\right) \left(\tanh^{2}{\left(x \right)} - 1\right)}{\tanh{\left(x \right)}} + \frac{6 \left(\tanh^{2}{\left(x \right)} - 1\right)^{3}}{\tanh^{4}{\left(x \right)}} - \frac{10 \left(\tanh^{2}{\left(x \right)} - 1\right)^{2}}{\tanh^{2}{\left(x \right)}} + \frac{3 \left(\tanh^{2}{\left(x \right)} - 1\right)}{\tanh^{2}{\left(x \right)}} + 4 \tanh^{2}{\left(x \right)} - 4 + \frac{1}{\tanh{\left(x \right)}}\right) e^{x}
Simplify
The graph
Derivative of 18*e^x/tanh(x)
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