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y=arctan(sqrt(x)-pi/4)
Derivada de la función/ arctan/ sqrt(x)/ y=arctan(sqrt(x)-pi/4)

Derivada de y=arctan(sqrt(x)-pi/4)

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

Ha introducido [src] 
    /  ___   pi\
atan|\/ x  - --|
    \        4 /
atan⁡(x−π4)\operatorname{atan}{\left(\sqrt{x} - \frac{\pi}{4} \right)} 
atan(sqrt(x) - pi/4)
Gráfica
02468-8-6-4-2-10102-2
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Trazar el gráfico f'(x)
Primera derivada [src] 
             1             
---------------------------
        /                2\
    ___ |    /  ___   pi\ |
2*\/ x *|1 + |\/ x  - --| |
        \    \        4 / /
12x((x−π4)2+1)\frac{1}{2 \sqrt{x} \left(\left(\sqrt{x} - \frac{\pi}{4}\right)^{2} + 1\right)}
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Segunda derivada [src] 
   /             /          ___\    \
   | 1         8*\-pi + 4*\/ x /    |
-4*|---- + -------------------------|
   | 3/2     /                    2\|
   |x        |     /          ___\ ||
   \       x*\16 + \-pi + 4*\/ x / //
-------------------------------------
                            2        
             /          ___\         
        16 + \-pi + 4*\/ x /
−4(8(4x−π)x((4x−π)2+16)+1x32)(4x−π)2+16- \frac{4 \left(\frac{8 \left(4 \sqrt{x} - \pi\right)}{x \left(\left(4 \sqrt{x} - \pi\right)^{2} + 16\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{\left(4 \sqrt{x} - \pi\right)^{2} + 16}
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Tercera derivada [src] 
  /                                                                                           2    \
  |                                             /          ___\                /          ___\     |
  | 3                  32                    24*\-pi + 4*\/ x /            128*\-pi + 4*\/ x /     |
2*|---- - ---------------------------- + -------------------------- + -----------------------------|
  | 5/2        /                    2\      /                    2\                               2|
  |x       3/2 |     /          ___\ |    2 |     /          ___\ |        /                    2\ |
  |       x   *\16 + \-pi + 4*\/ x / /   x *\16 + \-pi + 4*\/ x / /    3/2 |     /          ___\ | |
  \                                                                   x   *\16 + \-pi + 4*\/ x / / /
----------------------------------------------------------------------------------------------------
                                                           2                                        
                                            /          ___\                                         
                                       16 + \-pi + 4*\/ x /
2(24(4x−π)x2((4x−π)2+16)+128(4x−π)2x32((4x−π)2+16)2−32x32((4x−π)2+16)+3x52)(4x−π)2+16\frac{2 \left(\frac{24 \left(4 \sqrt{x} - \pi\right)}{x^{2} \left(\left(4 \sqrt{x} - \pi\right)^{2} + 16\right)} + \frac{128 \left(4 \sqrt{x} - \pi\right)^{2}}{x^{\frac{3}{2}} \left(\left(4 \sqrt{x} - \pi\right)^{2} + 16\right)^{2}} - \frac{32}{x^{\frac{3}{2}} \left(\left(4 \sqrt{x} - \pi\right)^{2} + 16\right)} + \frac{3}{x^{\frac{5}{2}}}\right)}{\left(4 \sqrt{x} - \pi\right)^{2} + 16}
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Gráfico
Derivada de y=arctan(sqrt(x)-pi/4)
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