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Derivative of:
Derivative of t-sint
Derivative of -3*x^3+2*x^2-x-5
Derivative of (x-4)
Derivative of x^4-1/5*cos(x)^(5)+2
Identical expressions
ctg(3x)^(two *x)
ctg(3x) to the power of (2 multiply by x)
ctg(3x) to the power of (two multiply by x)
ctg(3x)(2*x)
ctg3x2*x
ctg(3x)^(2x)
ctg(3x)(2x)
ctg3x2x
ctg3x^2x

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

Derivative of ctg(3x)^(2*x)

The solution

You have entered [src]

   2*x     
cot   (3*x)

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

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

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

Transform

Detail solution

Don't know the steps in finding this derivative.

But the derivative is

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

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Identical expressions

Derivative of ctg(3x)^(2*x)

The graph:

Piecewise:

The solution