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log(x)*atan(5*x)^4

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  • Derivative of:
  • Derivative of x^(4/5) Derivative of x^(4/5)
  • Derivative of log(x^2+5) Derivative of log(x^2+5)
  • Derivative of e^(-2*x) Derivative of e^(-2*x)
  • Derivative of asin(2*x) Derivative of asin(2*x)

  • Identical expressions

  • log(x)*atan(five *x)^ four
  • logarithm of (x) multiply by arc tangent of gent of (5 multiply by x) to the power of 4
  • logarithm of (x) multiply by arc tangent of gent of (five multiply by x) to the power of four
  • log(x)*atan(5*x)4
  • logx*atan5*x4
  • log(x)*atan(5*x)⁴
  • log(x)atan(5x)^4
  • log(x)atan(5x)4
  • logxatan5x4
  • logxatan5x^4

  • Similar expressions

  • log(x)*arctan(5*x)^4
The derivative of the function/ log(x)*atan(5*x)^4

Derivative of log(x)*atan(5*x)^4

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

The graph:

from to

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The solution

You have entered [src] 
           4     
log(x)*atan (5*x)
$$\log{\left(x \right)} \operatorname{atan}^{4}{\left(5 x \right)}$$ 
log(x)*atan(5*x)^4
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    4               3            
atan (5*x)   20*atan (5*x)*log(x)
---------- + --------------------
    x                     2      
                  1 + 25*x
$$\frac{20 \log{\left(x \right)} \operatorname{atan}^{3}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{\operatorname{atan}^{4}{\left(5 x \right)}}{x}$$
Simplify
The second derivative [src] 
           /      2                                                        \
    2      |  atan (5*x)   100*(-3 + 10*x*atan(5*x))*log(x)    40*atan(5*x)|
atan (5*x)*|- ---------- - -------------------------------- + -------------|
           |       2                            2               /        2\|
           |      x                  /        2\              x*\1 + 25*x /|
           \                         \1 + 25*x /                           /
$$\left(- \frac{100 \left(10 x \operatorname{atan}{\left(5 x \right)} - 3\right) \log{\left(x \right)}}{\left(25 x^{2} + 1\right)^{2}} + \frac{40 \operatorname{atan}{\left(5 x \right)}}{x \left(25 x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(5 x \right)}}{x^{2}}\right) \operatorname{atan}^{2}{\left(5 x \right)}$$
Simplify
The third derivative [src] 
  /                                  /                                                 2     2     \                                             \          
  |                                  |      2            3       45*x*atan(5*x)   100*x *atan (5*x)|                                             |          
  |                              500*|- atan (5*x) + --------- - -------------- + -----------------|*log(x)                                      |          
  |    3               2             |                       2             2                  2    |                                             |          
  |atan (5*x)   30*atan (5*x)        \               1 + 25*x      1 + 25*x           1 + 25*x     /          150*(-3 + 10*x*atan(5*x))*atan(5*x)|          
2*|---------- - -------------- + -------------------------------------------------------------------------- - -----------------------------------|*atan(5*x)
  |     3        2 /        2\                                             2                                                          2          |          
  |    x        x *\1 + 25*x /                                  /        2\                                                /        2\           |          
  \                                                             \1 + 25*x /                                              x*\1 + 25*x /           /
$$2 \left(\frac{500 \left(\frac{100 x^{2} \operatorname{atan}^{2}{\left(5 x \right)}}{25 x^{2} + 1} - \frac{45 x \operatorname{atan}{\left(5 x \right)}}{25 x^{2} + 1} - \operatorname{atan}^{2}{\left(5 x \right)} + \frac{3}{25 x^{2} + 1}\right) \log{\left(x \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{150 \left(10 x \operatorname{atan}{\left(5 x \right)} - 3\right) \operatorname{atan}{\left(5 x \right)}}{x \left(25 x^{2} + 1\right)^{2}} - \frac{30 \operatorname{atan}^{2}{\left(5 x \right)}}{x^{2} \left(25 x^{2} + 1\right)} + \frac{\operatorname{atan}^{3}{\left(5 x \right)}}{x^{3}}\right) \operatorname{atan}{\left(5 x \right)}$$
Simplify
The graph
Derivative of log(x)*atan(5*x)^4
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