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The derivative of the function/ erf(x)*tan(x)

Derivative of erf(x)*tan(x)

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

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The solution

You have entered [src] 
erf(x)*tan(x)
tan⁡(x)erf⁡(x)\tan{\left(x \right)} \operatorname{erf}{\left(x \right)} 
erf(x)*tan(x)
The graph
02468-8-6-4-2-1010-20002000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                            2       
                          -x        
/       2   \          2*e   *tan(x)
\1 + tan (x)/*erf(x) + -------------
                             ____   
                           \/ pi
(tan⁡2(x)+1)erf⁡(x)+2e−x2tan⁡(x)π\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{erf}{\left(x \right)} + \frac{2 e^{- x^{2}} \tan{\left(x \right)}}{\sqrt{\pi}}
Simplify
The second derivative [src] 
  /                                                 2          2       \
  |                                /       2   \  -x         -x        |
  |/       2   \                 2*\1 + tan (x)/*e      2*x*e   *tan(x)|
2*|\1 + tan (x)/*erf(x)*tan(x) + -------------------- - ---------------|
  |                                       ____                 ____    |
  \                                     \/ pi                \/ pi     /
2(−2xe−x2tan⁡(x)π+(tan⁡2(x)+1)tan⁡(x)erf⁡(x)+2(tan⁡2(x)+1)e−x2π)2 \left(- \frac{2 x e^{- x^{2}} \tan{\left(x \right)}}{\sqrt{\pi}} + \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \operatorname{erf}{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) e^{- x^{2}}}{\sqrt{\pi}}\right)
Simplify
The third derivative [src] 
  /                                                            2                    2                             2       \
  |                                           /       2   \  -x      /        2\  -x             /       2   \  -x        |
  |/       2   \ /         2   \          6*x*\1 + tan (x)/*e      2*\-1 + 2*x /*e   *tan(x)   6*\1 + tan (x)/*e   *tan(x)|
2*|\1 + tan (x)/*\1 + 3*tan (x)/*erf(x) - ---------------------- + ------------------------- + ---------------------------|
  |                                                 ____                       ____                         ____          |
  \                                               \/ pi                      \/ pi                        \/ pi           /
2(−6x(tan⁡2(x)+1)e−x2π+2(2x2−1)e−x2tan⁡(x)π+(tan⁡2(x)+1)(3tan⁡2(x)+1)erf⁡(x)+6(tan⁡2(x)+1)e−x2tan⁡(x)π)2 \left(- \frac{6 x \left(\tan^{2}{\left(x \right)} + 1\right) e^{- x^{2}}}{\sqrt{\pi}} + \frac{2 \left(2 x^{2} - 1\right) e^{- x^{2}} \tan{\left(x \right)}}{\sqrt{\pi}} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \tan^{2}{\left(x \right)} + 1\right) \operatorname{erf}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) e^{- x^{2}} \tan{\left(x \right)}}{\sqrt{\pi}}\right)
Simplify
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