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Derivative of:
Derivative of f(x)=x
Derivative of 5x^2
Derivative of cos(sqrt(x))
Derivative of 3*sqrt(x)
Identical expressions
cot(three *x)^(two *e^x)
cotangent of (3 multiply by x) to the power of (2 multiply by e to the power of x)
cotangent of (three multiply by x) to the power of (two multiply by e to the power of x)
cot(3*x)(2*ex)
cot3*x2*ex
cot(3x)^(2e^x)
cot(3x)(2ex)
cot3x2ex
cot3x^2e^x

The derivative of the function/ cot(3*x)^(2*e^x)

Derivative of cot(3x)^(2e^x)

The solution

You have entered [src]

             x
          2*e 
(cot(3*x))

\cot^{2 e^{x}}{\left(3 x \right)}

  /             x\
d |          2*e |
--\(cot(3*x))    /
dx

\frac{d}{d x} \cot^{2 e^{x}}{\left(3 x \right)}

Transform

Detail solution

Don't know the steps in finding this derivative.

But the derivative is

$\left(2 e^{x}\right)^{2 e^{x}} \left(\log{\left(2 e^{x} \right)} + 1\right)$
Now simplify:

$\left(4 e^{2 x}\right)^{e^{x}} \left(x + \log{\left(2 \right)} + 1\right)$

The answer is:

\left(4 e^{2 x}\right)^{e^{x}} \left(x + \log{\left(2 \right)} + 1\right)

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

             x /                       /          2     \  x\
          2*e  |   x                 2*\-3 - 3*cot (3*x)/*e |
(cot(3*x))    *|2*e *log(cot(3*x)) + -----------------------|
               \                             cot(3*x)       /

\left(2 e^{x} \log{\left(\cot{\left(3 x \right)} \right)} + \frac{2 \left(- 3 \cot^{2}{\left(3 x \right)} - 3\right) e^{x}}{\cot{\left(3 x \right)}}\right) \cot^{2 e^{x}}{\left(3 x \right)}

Simplify

The second derivative [src]

                 /                                     2                                                             2                   \   
               x |                      /       2     \      /       2     \     /                   /       2     \\                    |   
            2*e  |           2        9*\1 + cot (3*x)/    6*\1 + cot (3*x)/     |                 3*\1 + cot (3*x)/|   x                |  x
2*(cot(3*x))    *|18 + 18*cot (3*x) - ------------------ - ----------------- + 2*|-log(cot(3*x)) + -----------------| *e  + log(cot(3*x))|*e 
                 |                           2                  cot(3*x)         \                      cot(3*x)    /                    |   
                 \                        cot (3*x)                                                                                      /

2 \cdot \left(2 \left(- \log{\left(\cot{\left(3 x \right)} \right)} + \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}}\right)^{2} e^{x} + 18 \cot^{2}{\left(3 x \right)} + \log{\left(\cot{\left(3 x \right)} \right)} - \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} - \frac{6 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} + 18\right) e^{x} \cot^{2 e^{x}}{\left(3 x \right)}

Simplify

The third derivative [src]

                 /                                                                     3                     2                                                             3                           2                                          /                                                                          2\                   \   
               x |                                                      /       2     \       /       2     \      /       2     \     /                   /       2     \\             /       2     \      /                   /       2     \\ |                                       /       2     \     /       2     \ |                   |   
            2*e  |           2            /       2     \            54*\1 + cot (3*x)/    27*\1 + cot (3*x)/    9*\1 + cot (3*x)/     |                 3*\1 + cot (3*x)/|   2*x   108*\1 + cot (3*x)/      |                 3*\1 + cot (3*x)/| |                            2        6*\1 + cot (3*x)/   9*\1 + cot (3*x)/ |  x                |  x
2*(cot(3*x))    *|54 + 54*cot (3*x) - 108*\1 + cot (3*x)/*cot(3*x) - ------------------- - ------------------- - ----------------- - 4*|-log(cot(3*x)) + -----------------| *e    + -------------------- + 6*|-log(cot(3*x)) + -----------------|*|-18 - log(cot(3*x)) - 18*cot (3*x) + ----------------- + ------------------|*e  + log(cot(3*x))|*e 
                 |                                                           3                     2                  cot(3*x)         \                      cot(3*x)    /               cot(3*x)           \                      cot(3*x)    / |                                          cot(3*x)              2          |                   |   
                 \                                                        cot (3*x)             cot (3*x)                                                                                                                                         \                                                             cot (3*x)     /                   /

2 \left(- 4 \left(- \log{\left(\cot{\left(3 x \right)} \right)} + \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}}\right)^{3} e^{2 x} + 6 \cdot \left(- \log{\left(\cot{\left(3 x \right)} \right)} + \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}}\right) \left(- 18 \cot^{2}{\left(3 x \right)} - \log{\left(\cot{\left(3 x \right)} \right)} + \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} + \frac{6 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - 18\right) e^{x} - 108 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)} + 54 \cot^{2}{\left(3 x \right)} + \frac{108 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot{\left(3 x \right)}} + \log{\left(\cot{\left(3 x \right)} \right)} - \frac{54 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{3}}{\cot^{3}{\left(3 x \right)}} - \frac{27 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} - \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} + 54\right) e^{x} \cot^{2 e^{x}}{\left(3 x \right)}

Simplify

The graph

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Identical expressions

Derivative of cot(3x)^(2e^x)

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Derivative of cot(3*x)^(2*e^x)

The graph:

Piecewise:

The solution

Derivative of cot(3x)^(2e^x)