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y=arctan(4x+3)*arccos(x^3)
Derivada de la función/ arccos/ (x^3)/ arctan/ y=arctan(4x+3)*arccos(x^3)

Derivada de y=arctan(4x+3)*arccos(x^3)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
                  / 3\
atan(4*x + 3)*acos\x /
acos⁡(x3)atan⁡(4x+3)\operatorname{acos}{\left(x^{3} \right)} \operatorname{atan}{\left(4 x + 3 \right)} 
atan(4*x + 3)*acos(x^3)
Gráfica
02468-8-6-4-2-1010-2020
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Primera derivada [src] 
        / 3\        2              
  4*acos\x /     3*x *atan(4*x + 3)
-------------- - ------------------
             2         ________    
1 + (4*x + 3)         /      6     
                    \/  1 - x
−3x2atan⁡(4x+3)1−x6+4acos⁡(x3)(4x+3)2+1- \frac{3 x^{2} \operatorname{atan}{\left(4 x + 3 \right)}}{\sqrt{1 - x^{6}}} + \frac{4 \operatorname{acos}{\left(x^{3} \right)}}{\left(4 x + 3\right)^{2} + 1}
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Segunda derivada [src] 
                                                             /          6 \              
                                                             |       3*x  |              
                                                         3*x*|-2 + -------|*atan(3 + 4*x)
                   / 3\                  2                   |           6|              
  32*(3 + 4*x)*acos\x /              24*x                    \     -1 + x /              
- --------------------- - ---------------------------- + --------------------------------
                    2                         ________                ________           
    /             2\      /             2\   /      6                /      6            
    \1 + (3 + 4*x) /      \1 + (3 + 4*x) /*\/  1 - x               \/  1 - x
−24x21−x6((4x+3)2+1)+3x(3x6x6−1−2)atan⁡(4x+3)1−x6−32(4x+3)acos⁡(x3)((4x+3)2+1)2- \frac{24 x^{2}}{\sqrt{1 - x^{6}} \left(\left(4 x + 3\right)^{2} + 1\right)} + \frac{3 x \left(\frac{3 x^{6}}{x^{6} - 1} - 2\right) \operatorname{atan}{\left(4 x + 3 \right)}}{\sqrt{1 - x^{6}}} - \frac{32 \left(4 x + 3\right) \operatorname{acos}{\left(x^{3} \right)}}{\left(\left(4 x + 3\right)^{2} + 1\right)^{2}}
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Tercera derivada [src] 
    /         6          12  \                                                                                                                  
    |     27*x       27*x    |                     /                 2 \                     /          6 \                                     
  3*|2 - ------- + ----------|*atan(3 + 4*x)       |      4*(3 + 4*x)  |     / 3\            |       3*x  |                                     
    |          6            2|                 128*|-1 + --------------|*acos\x /       36*x*|-2 + -------|                                     
    |    -1 + x    /      6\ |                     |                  2|                     |           6|                    2                
    \              \-1 + x / /                     \     1 + (3 + 4*x) /                     \     -1 + x /               288*x *(3 + 4*x)      
- ------------------------------------------ + ---------------------------------- + ---------------------------- + -----------------------------
                    ________                                           2                                ________                   2    ________
                   /      6                            /             2\             /             2\   /      6    /             2\    /      6 
                 \/  1 - x                             \1 + (3 + 4*x) /             \1 + (3 + 4*x) /*\/  1 - x     \1 + (3 + 4*x) / *\/  1 - x
288x2(4x+3)1−x6((4x+3)2+1)2+36x(3x6x6−1−2)1−x6((4x+3)2+1)+128(4(4x+3)2(4x+3)2+1−1)acos⁡(x3)((4x+3)2+1)2−3(27x12(x6−1)2−27x6x6−1+2)atan⁡(4x+3)1−x6\frac{288 x^{2} \left(4 x + 3\right)}{\sqrt{1 - x^{6}} \left(\left(4 x + 3\right)^{2} + 1\right)^{2}} + \frac{36 x \left(\frac{3 x^{6}}{x^{6} - 1} - 2\right)}{\sqrt{1 - x^{6}} \left(\left(4 x + 3\right)^{2} + 1\right)} + \frac{128 \left(\frac{4 \left(4 x + 3\right)^{2}}{\left(4 x + 3\right)^{2} + 1} - 1\right) \operatorname{acos}{\left(x^{3} \right)}}{\left(\left(4 x + 3\right)^{2} + 1\right)^{2}} - \frac{3 \left(\frac{27 x^{12}}{\left(x^{6} - 1\right)^{2}} - \frac{27 x^{6}}{x^{6} - 1} + 2\right) \operatorname{atan}{\left(4 x + 3 \right)}}{\sqrt{1 - x^{6}}}
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Gráfico
Derivada de y=arctan(4x+3)*arccos(x^3)
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