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y=7arccosx/lnx
Derivada de la función/ x/lnx/ arccos/ y=7arccosx/lnx

Derivada de y=7arccosx/lnx

Función f() - derivada -er orden en el punto
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Solución

Ha introducido [src] 
7*acos(x)
---------
  log(x)
7acos⁡(x)log⁡(x)\frac{7 \operatorname{acos}{\left(x \right)}}{\log{\left(x \right)}} 
(7*acos(x))/log(x)
Gráfica
02468-8-6-4-2-10100-200
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
          7            7*acos(x)
- ------------------ - ---------
     ________               2   
    /      2           x*log (x)
  \/  1 - x  *log(x)
−71−x2log⁡(x)−7acos⁡(x)xlog⁡(x)2- \frac{7}{\sqrt{1 - x^{2}} \log{\left(x \right)}} - \frac{7 \operatorname{acos}{\left(x \right)}}{x \log{\left(x \right)}^{2}}
Simplificar
Segunda derivada [src] 
  /                                       /      2   \        \
  |                                       |1 + ------|*acos(x)|
  |       x                 2             \    log(x)/        |
7*|- ----------- + -------------------- + --------------------|
  |          3/2        ________                2             |
  |  /     2\          /      2                x *log(x)      |
  \  \1 - x /      x*\/  1 - x  *log(x)                       /
---------------------------------------------------------------
                             log(x)
7(−x(1−x2)32+2x1−x2log⁡(x)+(1+2log⁡(x))acos⁡(x)x2log⁡(x))log⁡(x)\frac{7 \left(- \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x \sqrt{1 - x^{2}} \log{\left(x \right)}} + \frac{\left(1 + \frac{2}{\log{\left(x \right)}}\right) \operatorname{acos}{\left(x \right)}}{x^{2} \log{\left(x \right)}}\right)}{\log{\left(x \right)}}
Simplificar
Tercera derivada [src] 
  /          2                                                                                 \
  |       3*x                                                    /      3         3   \        |
  |-1 + -------                              /      2   \      2*|1 + ------ + -------|*acos(x)|
  |           2                            3*|1 + ------|        |    log(x)      2   |        |
  |     -1 + x            3                  \    log(x)/        \             log (x)/        |
7*|------------ + ------------------ - --------------------- - --------------------------------|
  |        3/2            3/2                ________                      3                   |
  |/     2\       /     2\              2   /      2                      x *log(x)            |
  \\1 - x /       \1 - x /   *log(x)   x *\/  1 - x  *log(x)                                   /
------------------------------------------------------------------------------------------------
                                             log(x)
7(3x2x2−1−1(1−x2)32+3(1−x2)32log⁡(x)−3(1+2log⁡(x))x21−x2log⁡(x)−2(1+3log⁡(x)+3log⁡(x)2)acos⁡(x)x3log⁡(x))log⁡(x)\frac{7 \left(\frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}} \log{\left(x \right)}} - \frac{3 \left(1 + \frac{2}{\log{\left(x \right)}}\right)}{x^{2} \sqrt{1 - x^{2}} \log{\left(x \right)}} - \frac{2 \left(1 + \frac{3}{\log{\left(x \right)}} + \frac{3}{\log{\left(x \right)}^{2}}\right) \operatorname{acos}{\left(x \right)}}{x^{3} \log{\left(x \right)}}\right)}{\log{\left(x \right)}}
Simplificar
Gráfico
Derivada de y=7arccosx/lnx
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