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y=4^cosx*arctg2x
Derivada de la función/ ctg2x/ arctg/ 4^cosx/ y=4^cosx*arctg2x

Derivada de y=4^cosx*arctg2x

Función f() - derivada -er orden en el punto
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Ha introducido [src] 
 cos(x)          
4      *atan(2*x)
4cos⁡(x)atan⁡(2x)4^{\cos{\left(x \right)}} \operatorname{atan}{\left(2 x \right)} 
4^cos(x)*atan(2*x)
Gráfica
02468-8-6-4-2-1010-1010
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Trazar el gráfico f'(x)
Primera derivada [src] 
   cos(x)                                  
2*4          cos(x)                        
--------- - 4      *atan(2*x)*log(4)*sin(x)
        2                                  
 1 + 4*x
−4cos⁡(x)log⁡(4)sin⁡(x)atan⁡(2x)+2⋅4cos⁡(x)4x2+1- 4^{\cos{\left(x \right)}} \log{\left(4 \right)} \sin{\left(x \right)} \operatorname{atan}{\left(2 x \right)} + \frac{2 \cdot 4^{\cos{\left(x \right)}}}{4 x^{2} + 1}
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Segunda derivada [src] 
 cos(x) /      16*x      /             2          \                    4*log(4)*sin(x)\
4      *|- ----------- + \-cos(x) + sin (x)*log(4)/*atan(2*x)*log(4) - ---------------|
        |            2                                                            2   |
        |  /       2\                                                      1 + 4*x    |
        \  \1 + 4*x /                                                                 /
4cos⁡(x)(−16x(4x2+1)2+(log⁡(4)sin⁡2(x)−cos⁡(x))log⁡(4)atan⁡(2x)−4log⁡(4)sin⁡(x)4x2+1)4^{\cos{\left(x \right)}} \left(- \frac{16 x}{\left(4 x^{2} + 1\right)^{2}} + \left(\log{\left(4 \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(4 \right)} \operatorname{atan}{\left(2 x \right)} - \frac{4 \log{\left(4 \right)} \sin{\left(x \right)}}{4 x^{2} + 1}\right)
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Tercera derivada [src] 
        /   /          2  \                                                                                                                             \
        |   |      16*x   |                                                                                                                             |
        |16*|-1 + --------|                                                                                                                             |
        |   |            2|     /             2          \                                                                                              |
 cos(x) |   \     1 + 4*x /   6*\-cos(x) + sin (x)*log(4)/*log(4)   /       2       2                     \                           48*x*log(4)*sin(x)|
4      *|------------------ + ----------------------------------- + \1 - log (4)*sin (x) + 3*cos(x)*log(4)/*atan(2*x)*log(4)*sin(x) + ------------------|
        |             2                            2                                                                                               2    |
        |   /       2\                      1 + 4*x                                                                                      /       2\     |
        \   \1 + 4*x /                                                                                                                   \1 + 4*x /     /
4cos⁡(x)(48xlog⁡(4)sin⁡(x)(4x2+1)2+(−log⁡(4)2sin⁡2(x)+3log⁡(4)cos⁡(x)+1)log⁡(4)sin⁡(x)atan⁡(2x)+6(log⁡(4)sin⁡2(x)−cos⁡(x))log⁡(4)4x2+1+16(16x24x2+1−1)(4x2+1)2)4^{\cos{\left(x \right)}} \left(\frac{48 x \log{\left(4 \right)} \sin{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2}} + \left(- \log{\left(4 \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(4 \right)} \cos{\left(x \right)} + 1\right) \log{\left(4 \right)} \sin{\left(x \right)} \operatorname{atan}{\left(2 x \right)} + \frac{6 \left(\log{\left(4 \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(4 \right)}}{4 x^{2} + 1} + \frac{16 \left(\frac{16 x^{2}}{4 x^{2} + 1} - 1\right)}{\left(4 x^{2} + 1\right)^{2}}\right)
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Gráfico
Derivada de y=4^cosx*arctg2x
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