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y=sin(exp(x)+4√(x)+arctan(2x))
Derivada de la función/ y=sin(exp(x)+4√(x)+arctan(2x))

Derivada de y=sin(exp(x)+4√(x)+arctan(2x))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   / x       ___            \
sin\e  + 4*\/ x  + atan(2*x)/
sin⁡((4x+ex)+atan⁡(2x))\sin{\left(\left(4 \sqrt{x} + e^{x}\right) + \operatorname{atan}{\left(2 x \right)} \right)} 
sin(exp(x) + 4*sqrt(x) + atan(2*x))
Gráfica
02468-8-6-4-2-1010-5000050000
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Primera derivada [src] 
/  2        2        x\    / x       ___            \
|----- + -------- + e |*cos\e  + 4*\/ x  + atan(2*x)/
|  ___          2     |                              
\\/ x    1 + 4*x      /
(ex+24x2+1+2x)cos⁡((4x+ex)+atan⁡(2x))\left(e^{x} + \frac{2}{4 x^{2} + 1} + \frac{2}{\sqrt{x}}\right) \cos{\left(\left(4 \sqrt{x} + e^{x}\right) + \operatorname{atan}{\left(2 x \right)} \right)}
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Segunda derivada [src] 
 /                       2                                                                                        \
 |/  2        2        x\     /    ___                x\   / 1      x       16*x   \    /    ___                x\|
-||----- + -------- + e | *sin\4*\/ x  + atan(2*x) + e / + |---- - e  + -----------|*cos\4*\/ x  + atan(2*x) + e /|
 ||  ___          2     |                                  | 3/2                  2|                              |
 |\\/ x    1 + 4*x      /                                  |x           /       2\ |                              |
 \                                                         \            \1 + 4*x / /                              /
−((16x(4x2+1)2−ex+1x32)cos⁡(4x+ex+atan⁡(2x))+(ex+24x2+1+2x)2sin⁡(4x+ex+atan⁡(2x)))- (\left(\frac{16 x}{\left(4 x^{2} + 1\right)^{2}} - e^{x} + \frac{1}{x^{\frac{3}{2}}}\right) \cos{\left(4 \sqrt{x} + e^{x} + \operatorname{atan}{\left(2 x \right)} \right)} + \left(e^{x} + \frac{2}{4 x^{2} + 1} + \frac{2}{\sqrt{x}}\right)^{2} \sin{\left(4 \sqrt{x} + e^{x} + \operatorname{atan}{\left(2 x \right)} \right)})
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Tercera derivada [src] 
/                                      2  \                                                                                                                                                                           
|       32          x    3        512*x   |    /    ___                x\                                                                                                                                             
|- ----------- + 2*e  + ---- + -----------|*cos\4*\/ x  + atan(2*x) + e /                                                                                                                                             
|            2           5/2             3|                                                                                                                                                                           
|  /       2\           x      /       2\ |                                                        3                                                                                                                  
\  \1 + 4*x /                  \1 + 4*x / /                                 /  2        2        x\     /    ___                x\     / 1      x       16*x   \ /  2        2        x\    /    ___                x\
------------------------------------------------------------------------- - |----- + -------- + e | *cos\4*\/ x  + atan(2*x) + e / + 3*|---- - e  + -----------|*|----- + -------- + e |*sin\4*\/ x  + atan(2*x) + e /
                                    2                                       |  ___          2     |                                    | 3/2                  2| |  ___          2     |                              
                                                                            \\/ x    1 + 4*x      /                                    |x           /       2\ | \\/ x    1 + 4*x      /                              
                                                                                                                                       \            \1 + 4*x / /
3(16x(4x2+1)2−ex+1x32)(ex+24x2+1+2x)sin⁡(4x+ex+atan⁡(2x))−(ex+24x2+1+2x)3cos⁡(4x+ex+atan⁡(2x))+(512x2(4x2+1)3+2ex−32(4x2+1)2+3x52)cos⁡(4x+ex+atan⁡(2x))23 \left(\frac{16 x}{\left(4 x^{2} + 1\right)^{2}} - e^{x} + \frac{1}{x^{\frac{3}{2}}}\right) \left(e^{x} + \frac{2}{4 x^{2} + 1} + \frac{2}{\sqrt{x}}\right) \sin{\left(4 \sqrt{x} + e^{x} + \operatorname{atan}{\left(2 x \right)} \right)} - \left(e^{x} + \frac{2}{4 x^{2} + 1} + \frac{2}{\sqrt{x}}\right)^{3} \cos{\left(4 \sqrt{x} + e^{x} + \operatorname{atan}{\left(2 x \right)} \right)} + \frac{\left(\frac{512 x^{2}}{\left(4 x^{2} + 1\right)^{3}} + 2 e^{x} - \frac{32}{\left(4 x^{2} + 1\right)^{2}} + \frac{3}{x^{\frac{5}{2}}}\right) \cos{\left(4 \sqrt{x} + e^{x} + \operatorname{atan}{\left(2 x \right)} \right)}}{2}
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Gráfico
Derivada de y=sin(exp(x)+4√(x)+arctan(2x))
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