Derivada de y=5arctg2x*lnx2

Ha introducido [src]

5*atan(2*x)*log(x)*2

2 \log{\left(x \right)} 5 \operatorname{atan}{\left(2 x \right)}

((5*atan(2*x))*log(x))*2

Gráfica

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Primera derivada [src]

10*atan(2*x)   20*log(x)
------------ + ---------
     x                 2
                1 + 4*x

\frac{20 \log{\left(x \right)}}{4 x^{2} + 1} + \frac{10 \operatorname{atan}{\left(2 x \right)}}{x}

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Segunda derivada [src]

   /  atan(2*x)        4         16*x*log(x)\
10*|- --------- + ------------ - -----------|
   |       2        /       2\             2|
   |      x       x*\1 + 4*x /   /       2\ |
   \                             \1 + 4*x / /

10 \left(- \frac{16 x \log{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{4}{x \left(4 x^{2} + 1\right)} - \frac{\operatorname{atan}{\left(2 x \right)}}{x^{2}}\right)

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Tercera derivada [src]

   /                                              /          2  \       \
   |                                              |      16*x   |       |
   |                                            8*|-1 + --------|*log(x)|
   |                                              |            2|       |
   |       24       atan(2*x)         3           \     1 + 4*x /       |
20*|- ----------- + --------- - ------------- + ------------------------|
   |            2        3       2 /       2\                   2       |
   |  /       2\        x       x *\1 + 4*x /         /       2\        |
   \  \1 + 4*x /                                      \1 + 4*x /        /

20 \left(\frac{8 \left(\frac{16 x^{2}}{4 x^{2} + 1} - 1\right) \log{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2}} - \frac{24}{\left(4 x^{2} + 1\right)^{2}} - \frac{3}{x^{2} \left(4 x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(2 x \right)}}{x^{3}}\right)

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Gráfico

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Derivada de y=5arctg2x*lnx2

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